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Length of a shortest cycle contained in the graph
In graph theory, the girth of an undirected graph is the length of a shortest cycle contained in the graph. If the graph does not contain any cycles (that
Girth_(graph_theory)
Regular graph with girth more than twice its diameter
Moore graph with girth 5 and degree 57 exist? More unsolved problems in mathematics In graph theory, a Moore graph is a regular graph whose girth (the
Moore_graph
Topics referred to by the same term
space Girth (geometry), the perimeter of a parallel projection of a shape Girth (graph theory), the length of a shortest cycle contained in a graph Matroid
Girth
Trail in which only the first and last vertices are equal
In graph theory, a cycle in a graph is a non-empty trail in which only the first and last vertices are equal. A directed cycle in a directed graph is
Cycle_(graph_theory)
Appendix:Glossary of graph theory in Wiktionary, the free dictionary. This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes
Glossary_of_graph_theory
Longest distance between two vertices
depending on the degree. The girth of a graph, the length of its shortest cycle, can be at most 2 k + 1 {\displaystyle 2k+1} for a graph of diameter k {\displaystyle
Diameter_(graph_theory)
Triangle-free graph requiring four colors
In the mathematical field of graph theory, the Grötzsch graph is a triangle-free graph with 11 vertices, 20 edges, chromatic number 4, and crossing number
Grötzsch_graph
Subgraph induced by all nodes linked to a given node of a graph
In graph theory, the neighbourhood of a vertex v in a graph G is the subgraph of G induced by all the vertices that are connected to v by an edge (vertices
Neighbourhood_(graph_theory)
Cubic graph with 10 vertices and 15 edges
bridgeless graph has a cycle-continuous mapping to the Petersen graph. More unsolved problems in mathematics In the mathematical field of graph theory, the
Petersen_graph
Tree graph with one central node and leaves of length 1
In graph theory, the star Sk is the complete bipartite graph K1, k, that is, it is a tree with one internal node and k leaves. Alternatively, some authors
Star_(graph_theory)
Methodic assignment of colors to elements of a graph
In graph theory, graph coloring is a methodic assignment of labels traditionally called "colors" to elements of a graph. The assignment is subject to certain
Graph_coloring
Graph representing faces of another graph
mathematical discipline of graph theory, the dual graph of a planar graph G is a graph that has a vertex for each face of G. The dual graph has an edge for each
Dual_graph
Regular graph with fewest possible nodes for its girth
of graph theory, a cage is a regular graph that has as few vertices as possible for its girth. Formally, an (r, g)-graph is defined to be a graph in which
Cage_(graph_theory)
Spectral graph theory concept
spectral graph theory, a Ramanujan graph is a regular graph whose spectral gap is almost as large as possible (see extremal graph theory). Such graphs are
Ramanujan_graph
Graph of triangles with a shared vertex
the mathematical field of graph theory, the friendship graph (or Dutch windmill graph or n-fan) Fn is a planar, undirected graph with 2n + 1 vertices and
Friendship_graph
discrete and Euclidean geometries, graph theory, group theory, mathematical logic, number theory, set theory, Ramsey theory, dynamical systems, and partial
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Undirected graph with 14 vertices
in the graph have six or more edges. Every smaller cubic graph has shorter cycles, so this graph is the 6-cage, the smallest cubic graph of girth 6. It
Heawood_graph
3-regular graph with no 3-edge-coloring
In the mathematical field of graph theory, a snark is an undirected graph with exactly three edges per vertex whose edges cannot be colored with only three
Snark_(graph_theory)
Robertson graph is the unique (4,5)-cage graph and was discovered by Robertson in 1964. As a cage graph, it is the smallest 4-regular graph with girth 5. It
Robertson_graph
Graph in which every two vertices are adjacent
In the mathematical field of graph theory, a complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique
Complete_graph
Structure-preserving correspondence between node-link graphs
In the mathematical field of graph theory, a graph homomorphism is a mapping between two graphs that respects their structure. More concretely, it is a
Graph_homomorphism
Graph without triples of adjacent vertices
equivalently defined as graphs with clique number ≤ 2, graphs with girth ≥ 4, graphs with no induced 3-cycle, or locally independent graphs. By Turán's theorem
Triangle-free_graph
Planar graph with 5 nodes and 6 edges
mathematical field of graph theory, the butterfly graph (also called the bowtie graph and the hourglass graph) is a planar, undirected graph with 5 vertices
Butterfly_graph
Property of graphs that depends only on abstract structure
In graph theory, a graph property or graph invariant is a property of graphs that depends only on the abstract structure, not on graph representations
Graph_property
Planar graph with 4 nodes and 5 edges
K 4 {\displaystyle K_{4}} minus one edge. The diamond graph has radius 1, diameter 2, girth 3, chromatic number 3 and chromatic index 3. It is also
Diamond_graph
Bivariegated graph Cage (graph theory) Cayley graph Circle graph Clique graph Cograph Common graph Complement of a graph Complete graph Cubic graph Cycle graph De
List_of_graph_theory_topics
Graph with edges of length one, able to be drawn without crossings
In geometric graph theory, a branch of mathematics, a matchstick graph is a graph that can be drawn in the plane in such a way that its edges are line
Matchstick_graph
mathematics, in the realm of group theory, a group is said to be thin if there is a finite upper bound on the girth of the Cayley graph induced by any finite generating
Thin group (combinatorial group theory)
Thin_group_(combinatorial_group_theory)
Family of symmetric graphs which generalize the Petersen graph
systems. They include and generalize the Petersen graph. The odd graphs have high odd girth, meaning that they contain long odd-length cycles but no short
Odd_graph
Type of graph in graph theory
mathematical field of graph theory, a graph G is said to be hypohamiltonian if G itself does not have a Hamiltonian cycle but every graph formed by removing
Hypohamiltonian_graph
7-regular undirected graph with 50 nodes and 175 edges
of graph theory, the Hoffman–Singleton graph is a 7-regular undirected graph with 50 vertices and 175 edges. It is the unique strongly regular graph with
Hoffman–Singleton_graph
Longest distance between tree vertices
In graph theory, the triameter is a metric invariant that generalizes the concept of a graph's diameter. It is defined as the maximum sum of pairwise
Triameter_(graph_theory)
Graph whose vertices correspond to combinations of a set of n elements
In graph theory, the Kneser graph K(n, k) (alternatively KGn,k) is the graph whose vertices correspond to the k-element subsets of a set of n elements
Kneser_graph
Graph divided into two independent sets
In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets
Bipartite_graph
has chromatic number 3, chromatic index 3, girth 4 and diameter 8. The Tutte graph is a cubic polyhedral graph, but is non-hamiltonian. Therefore, it is
Tutte_graph
Planar bipartite graph with 25 vertices and 31 edges
chromatic index 3, girth 3 and diameter 8. If the single vertex of degree 1 whose neighbour has degree 3 is removed, the resulting graph has no Hamiltonian
Walther_graph
Family of cubic graphs formed from regular and star polygons
In graph theory, the generalized Petersen graphs are a family of cubic graphs formed by connecting the vertices of a regular polygon to the corresponding
Generalized_Petersen_graph
Graph in which all ordered pairs of linked nodes are automorphic
In the mathematical field of graph theory, a graph G is symmetric or arc-transitive if, given any two ordered pairs of adjacent vertices ( u 1 , v 1 )
Symmetric_graph
Distance-transitive cubic graph with 20 nodes and 30 edges
In the mathematical field of graph theory, the Desargues graph is a distance-transitive, cubic graph with 20 vertices and 30 edges. It is named after
Desargues_graph
Undirected bipartite graph with 112 vertices and 168 edges
capital of Slovenia). It is a cubic graph with diameter 8, radius 7, chromatic number 2 and chromatic index 3. Its girth is 10 and there are exactly 168 cycles
Ljubljana_graph
Graph with nodes connected in a closed chain
In graph theory, a cycle graph or circular graph is a graph that consists of a single cycle, or in other words, some number of vertices (at least 3, if
Cycle_graph
is triangle-free, 4-regular, and 4-chromatic. The Chvátal graph is triangle-free: its girth (the length of its shortest cycle) is four. It is 4-regular:
Chvátal_graph
Two special graphs in graph theory
In the mathematical field of graph theory, the Klein graphs are two different but related regular graphs, each with 84 edges. Each can be embedded in
Klein_graphs
Planar, undirected graph with 2n vertices and 3n-2 edges
mathematical field of graph theory, the ladder graph Ln is a planar, undirected graph with 2n vertices and 3n − 2 edges. The ladder graph can be obtained as
Ladder_graph
Concept in graph theory
In graph theory, a strongly regular graph (SRG) is a regular graph G = (V, E) with v vertices and degree k such that for some given integers λ , μ ≥ 0
Strongly_regular_graph
Graph which remains connected when fewer than k edges are removed
graph theory, a connected graph is k-edge-connected if it remains connected whenever fewer than k edges are removed. The edge-connectivity of a graph
Edge_connectivity
Graph with 24 vertices and 36 edges
smallest cubic graph of girth 7). It is also the smallest cubic cage that is not a Moore graph. First discovered by Sachs but unpublished, the graph is named
McGee_graph
Cycle graph plus universal vertex
In graph theory, a wheel graph is a graph formed by connecting a single universal vertex to all vertices of a cycle. A wheel graph with n vertices can
Wheel_graph
Bipartite graph where each node of 1st set is linked to all nodes of 2nd set
In the mathematical field of graph theory, a complete bipartite graph or biclique is a special kind of bipartite graph where every vertex of the first
Complete_bipartite_graph
Graph where any two nodes of equal distance are isomorphic
In the mathematical field of graph theory, a distance-transitive graph is a graph such that, given any two vertices v and w at any distance i, and any
Distance-transitive_graph
mathematical graph theory, the Higman–Sims graph is a 22-regular undirected graph with 100 vertices and 1100 edges. It is the unique strongly regular graph srg(100
Higman–Sims_graph
Intersection graph of a chord diagram
In graph theory, a circle graph is the intersection graph of a chord diagram. That is, it is an undirected graph whose vertices can be associated with
Circle_graph
as induced subgraphs produce graphs of bounded chromatic number? More unsolved problems in mathematics In graph theory, the Gyárfás–Sumner conjecture
Gyárfás–Sumner_conjecture
Concept in graph theory
In the mathematical field of graph theory, the pancake graph Pn or n-pancake graph is a graph whose vertices are the permutations of n symbols from 1 to
Pancake_graph
Number of planar subgraphs to cover a graph
In graph theory, the thickness of a graph G is the minimum number of planar graphs into which the edges of G can be partitioned. That is, if there exists
Thickness_(graph_theory)
diameter 3 and girth 5. It is also a 3-vertex-connected graph and a 3-edge-connected graph. It is the smallest 4-regular graph of girth 5 with chromatic
Brinkmann_graph
Graph made from a subset of another graph's nodes and their edges
In graph theory, an induced subgraph of a graph is another graph, formed from a subset of the vertices of the graph and all of the edges, from the original
Induced_subgraph
diameter 5 and girth 6. It is also a 3-vertex-connected and a 3-edge-connected graph. It has book thickness 3 and queue number 2. The graph is 1-planar.
Dyck_graph
configuration if and only if its girth is at least six. Scheinerman, Edward R.; Ullman, Daniel H. (1997), Fractional graph theory, Wiley-Interscience Series
Biregular_graph
Cubic graph with 8 vertices and 12 edges
mathematical field of graph theory, the Wagner graph is a 3-regular graph with 8 vertices and 12 edges. It is the 8-vertex Möbius ladder graph. As a Möbius ladder
Wagner_graph
Periodic spatial graph
the Laves graph is the space group I 4 1 32 {\displaystyle I4_{1}32} . The girth of this structure is 10—the shortest cycles in the graph have 10 vertices—and
Laves_graph
Graphs formed by a hypercube's edges and vertices
In graph theory, the hypercube graph Q n {\displaystyle Q_{n}} is the edge graph of the n {\displaystyle n} -dimensional hypercube, that is, it is the
Hypercube_graph
On coloring infinite graphs
In graph theory, the De Bruijn–Erdős theorem relates graph coloring of an infinite graph to the same problem on its finite subgraphs. It states that,
De Bruijn–Erdős theorem (graph theory)
De_Bruijn–Erdős_theorem_(graph_theory)
Graph with equal-size maximal independent sets
of the well-covered cubic graphs, well-covered claw-free graphs, and well-covered graphs of high girth allow these graphs to be recognized in polynomial
Well-covered_graph
Regular graph with 70 nodes and 105 edges
radius 6, diameter 6, girth 10 and is Hamiltonian. It is also a 3-vertex-connected and 3-edge-connected, non-planar, cubic graph. It has book thickness
Harries_graph
Abstraction of graph shortest cycles
representation. The "girth" terminology generalizes the use of girth in graph theory, meaning the length of the shortest cycle in a graph: the girth of a graphic
Matroid_girth
Graph path which is an induced subgraph
In the mathematical area of graph theory, an induced path in an undirected graph G is a path that is an induced subgraph of G. That is, it is a sequence
Induced_path
mathematical field of graph theory, the Harries–Wong graph is a 3-regular undirected graph with 70 vertices and 105 edges. The Harries–Wong graph has chromatic
Harries–Wong_graph
Cubic graph with 28 vertices and 42 edges
graph has chromatic number 3, chromatic index 3, radius 4, diameter 4 and girth 7. It is also a 3-vertex-connected graph and a 3-edge-connected graph
Coxeter_graph
various individual (finite) graphs. The columns 'vertices', 'edges', 'radius', 'diameter', 'girth', 'P' (whether the graph is planar), χ (chromatic number)
List of graphs by edges and vertices
List_of_graphs_by_edges_and_vertices
Type of graph in mathematical graph theory
discipline of graph theory, the (m,n)-lollipop graph is a special type of graph consisting of a complete graph (clique) on m vertices and a path graph on n vertices
Lollipop_graph
Graph where every edge is in one triangle
In graph theory, a locally linear graph is an undirected graph in which every edge belongs to exactly one triangle. Equivalently, for each vertex of the
Locally_linear_graph
Balanced complete multipartite graph
number of edges in a graph that does not have a fixed Turán graph as a subgraph. Via this theorem, similar bounds in extremal graph theory can be proven for
Turán_graph
Unproven conjecture in graph theory
mathematics Must every cubic graph contain a simple cycle of length a power of two? More unsolved problems in mathematics In graph theory, the unproven Erdős–Gyárfás
Erdős–Gyárfás_conjecture
Undirected graph with 11 nodes and 27 edges
In the mathematical field of graph theory, the Goldner–Harary graph is a simple undirected graph with 11 vertices and 27 edges. It is named after Anita
Goldner–Harary_graph
4-regular undirected graph with 70 vertices and 140 edges
The Meredith graph is 4-vertex-connected and 4-edge-connected, has chromatic number 3, chromatic index 5, radius 7, diameter 8, girth 4 and is non-Hamiltonian
Meredith_graph
Order-zero graph or any edgeless graph
mathematical field of graph theory, the term "null graph" may refer either to the order-zero graph, or alternatively, to any edgeless graph (the latter is sometimes
Null_graph
16-regular graph with 27 vertices and 216 edges
the mathematical field of graph theory, the Schläfli graph, named after Ludwig Schläfli, is a 16-regular undirected graph with 27 vertices and 216 edges
Schläfli_graph
On existence of a strongly regular graph
exist a strongly regular graph with parameters (99,14,1,2)? More unsolved problems in mathematics In graph theory, Conway's 99-graph problem is an unsolved
Conway's_99-graph_problem
Graph family made by joining complete graphs at a universal node
field of graph theory, the windmill graph Wd(k,n) is an undirected graph constructed for k ≥ 2 and n ≥ 2 by joining n copies of the complete graph Kk at
Windmill_graph
Family of triangle-free circulant graphs
In graph theory, an Andrásfai graph is a triangle-free, circulant graph named after Béla Andrásfai. The Andrásfai graph And(n) for any natural number n
Andrásfai_graph
Class of mathematical games
mathematical game related to graph theory. Coloring game problems arose as game-theoretic versions of well-known graph coloring problems. In a coloring
Graph_coloring_game
Constructs with triply-connected vertices
pictures contain girth, diameter, Wiener index, Estrada index and Kirchhoff index. Aut is the order of the Automorphism group of the graph. A Hamiltonian
Table_of_simple_cubic_graphs
field of graph theory, the triangle graph is a planar undirected graph with 3 vertices and 3 edges, in the form of a triangle. The triangle graph is also
Triangle_graph
Cycles in a graph that cover each edge twice
every bridgeless graph have a multiset of cycles covering every edge exactly twice? More unsolved problems in mathematics In graph-theoretic mathematics
Cycle_double_cover
Derived graph of higher chromatic number
In the mathematical area of graph theory, the Mycielskian or Mycielski graph of an undirected graph is a larger graph formed from it by a construction
Mycielskian
Number of cops needed to catch a robber on a graph
In graph theory, a branch of mathematics, the cop number or copnumber of an undirected graph is the minimum number of cops that suffices to ensure a win
Cop_number
the mathematical field of graph theory, the Dejter graph is a 6-regular graph with 112 vertices and 336 edges. The Dejter graph is obtained by deleting
Dejter_graph
mathematical field of graph theory, the Gray graph is an undirected bipartite graph with 54 vertices and 81 edges. It is a cubic graph: every vertex touches
Gray_graph
Graph with a triangular truncated trapezohedron as its skeleton
from 72° to 82°. The Dürer graph is the graph formed by the vertices and edges of the Dürer solid. It is a cubic graph of girth 3 and diameter 4. As well
Dürer_graph
Measure of distance in physical space
define the shortest path, girth (shortest cycle length), and longest path between two vertices in a graph. In measure theory, length is most often generalised
Length
Cubic graph with 12 vertices and 18 edges
In graph theory, the Frucht graph is a cubic graph with 12 vertices, 18 edges, and no nontrivial symmetries. It was first described by Robert Frucht in
Frucht_graph
Undirected cubic graph with 12 vertices and 18 edges
In the mathematical field of graph theory, Tietze's graph is an undirected cubic graph with 12 vertices and 18 edges. It is named after Heinrich Franz
Tietze's_graph
Cubic distance-regular graph with 102 nodes and 153 edges
girth 9. It is also a 3-vertex-connected graph and a 3-edge-connected graph. All the cubic distance-regular graphs are known. The Biggs–Smith graph is
Biggs–Smith_graph
Unsolved problem in extremal graph theory
maximum number of edges in a bipartite graph with n {\displaystyle n} vertices on each side that has no 4-cycle (its girth is six or more). Thus, z ( 2 ; 2
Zarankiewicz_problem
24-vertex symmetric bipartite cubic graph
In the mathematical field of graph theory, the Nauru graph is a symmetric, bipartite, cubic graph with 24 vertices and 36 edges. It was named by David
Nauru_graph
3-regular graph with 30 vertices and 45 edges
unique smallest cubic graph of girth 8, it is a cage and a Moore graph. It is bipartite, and can be constructed as the Levi graph of the generalized quadrangle
Tutte–Coxeter_graph
Infinite family of graphs
In the mathematical field of graph theory, the flower snarks form an infinite family of snarks introduced by Rufus Isaacs in 1975. As snarks, the flower
Flower_snark
discipline of graph theory, the (m,n)-tadpole graph is a special type of graph consisting of a cycle graph on m (at least 3) vertices and a path graph on n vertices
Tadpole_graph
Graph often embedded in the Klein bottle
mathematical field of graph theory, the Franklin graph is a 3-regular graph with 12 vertices and 18 edges. The Franklin graph is named after Philip Franklin
Franklin_graph
GIRTH GRAPH-THEORY
GIRTH GRAPH-THEORY
Boy/Male
Christian & English(British/American/Australian)
Herdsman
Boy/Male
African, Arabic
Grape Vines
Boy/Male
Norse American Swedish Scandinavian English
Defender.
Boy/Male
Muslim
Grape
Surname or Lastname
English and Scottish
English and Scottish : topographic name from Old English (ge)fyrhþe ‘woodland’ or ‘scrubland on the edge of a forest’.Scottish : habitational name from Firth in Orkney.Welsh : topographic name from Welsh ffrith, ffridd ‘barren land’, ‘mountain pasture’ (a borrowing of the Old English word mentioned in 1).
Boy/Male
Gujarati, Hindu, Indian, Jain, Kannada, Marathi, Telugu, Traditional
Holy Place; Pilgrim; To Go Yatra Dham; Tour to Holy Place
Boy/Male
Hindu
Holy place, Sacred water, Place of pilgrimage
Girl/Female
Arabic, Assamese, Hindu, Indian, Kannada, Malayalam, Marathi, Muslim, Telugu
Grape
Male
Welsh
 Contracted form of Welsh Gareth, possibly GARTH means "old." Compare with another form of Garth.
Boy/Male
Australian, British, English, Scottish
Arm of the Sea; Forest
Boy/Male
Hindu, Indian
Lord of Mountains
Girl/Female
Muslim
Grape like
Boy/Male
Hebrew, Hindu, Indian, Marathi
Grape Cluster
Girl/Female
Indian
Grape like
Boy/Male
Indian
Grape
Girl/Female
Indian
Grape vine
Boy/Male
Arabic, Modern
Grape
Boy/Male
English Scottish
Forest.
Girl/Female
Muslim
Grape vine
Boy/Male
American, Anglo, Australian, British, Christian, English, German, Indian, Norse, Scandinavian
Keeper of the Garden; An Enclosed Yard; Garden; Protection; Enclosure
GIRTH GRAPH-THEORY
GIRTH GRAPH-THEORY
Boy/Male
Arabic, Muslim
A Land of Prophet Ebrahim and his Descendant
Boy/Male
Hindu
Lord Vishnu
Girl/Female
Indian
Warner, Observer, Supervisor
Boy/Male
Tamil
Valmeki | வாலà¯à®®à¯€à®•à®¿
An ancient saint
Girl/Female
Muslim
Snow white
Girl/Female
Tamil
Pradyuta | பà¯à®°à®¤à¯à®¯à¯à®¤à®¾
To begin to shine
Girl/Female
German
Noble; Kind
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit
To End Evil or Bad; Lord Ganesha
Girl/Female
Arabic
Rose
Male
English
Candlemaker
GIRTH GRAPH-THEORY
GIRTH GRAPH-THEORY
GIRTH GRAPH-THEORY
GIRTH GRAPH-THEORY
GIRTH GRAPH-THEORY
n.
A birth.
n.
A girth.
n.
Same as Girth.
v. t.
To bind as with a girth.
n.
The act or fact of coming into life, or of being born; -- generally applied to human beings; as, the birth of a son.
n.
A small horizontal brace or girder.
n.
The act of bringing forth; as, she had two children at a birth.
n.
Lineage; extraction; descent; sometimes, high birth; noble extraction.
a.
Resembling a grape.
n.
A sort of grape.
n.
Lawful birth.
n.
A band or strap which encircles the body; especially, one by which a saddle is fastened upon the back of a horse.
a.
Birth; condition; rank by birth.
n.
A seed of the grape.
n.
A close; a yard; a croft; a garden; as, a cloister garth.
v.
To gird; to encircle; to invest by means of a girdle; to measure the girth of; as, to girt a tree.
n.
Origin; beginning; as, the birth of an empire.
n.
The measure round the body, as at the waist or belly; the circumference of anything.
a.
Without mirth.