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Moo-Ai is thinking... Processing hyper-cognitive insights for 'graph'
Recognition of chordal graphs and cographs which are Cover-Incomp...
vol. 26:320241210.46298/dmtcs.116572023-07-27; 2023-07-27; 2024-04-11; 2024-09-232024-10-02 Cover-Incomparability graphs (C-I graphs) are an interesting class of graphs from posets. A C-I graph is a g...
Perfect Graph -- from Wolfram MathWorld
A perfect graph is agraphsuch that for everyinduced
subgraphof,
theclique numberequals thechromatic
number, i.e.,.
A graph that is not a perfect graph is called animperfect
graph(Godsil and Royle...
Graceful Graph -- from Wolfram MathWorld
A graceful graph is a graph that can begracefully labeled. Special cases of graceful graphs include theutility
graph(Gardner 1983) andPetersen graph. A graph that
cannot begracefully labeledis calle...
Distance-Transitive Graph -- from Wolfram MathWorld
A graphis distance transitive if itsautomorphism groupistransitiveon pairs of vertices at each pairwise
distance in the graph. Distance-transitivity is a generalization ofdistance-regularity. Every d...
Matchstick Graph -- from Wolfram MathWorld
A matchstick graph is a simple graph which has agraph embeddingthat isplanar, for which all distances
between vertices have unit distance, and which is non-degenerate (so no vertices
are coincident,...
Graph in Data Structure | Types & Explanation
Lesson 38 of 63ByRavikiran A S Graphs in data structures are non-lineardata structuresmade up of a finite number of nodes or vertices and the edges that connect them. Graphs in data structures are use...
Petersen Graph -- from Wolfram MathWorld
The Petersen graph is thecubic graphon 10 vertices and 15 edges which is the unique-cage graph(Harary 1994,
p. 175), as well as the unique-Moore graph. It can be
constructed as thegraph expansionofw...
Bipartite Graph -- from Wolfram MathWorld
A bipartite graph, also called a bigraph, is a set ofgraph verticesdecomposed into two disjoint sets such that no twograph
verticeswithin the same set are adjacent. A bipartite graph is a special cas...
Distance-Regular Graph -- from Wolfram MathWorld
Aconnected graphis distance-regular if for any verticesandofand any integers, 1, ...(whereis thegraph diameter),
the number of vertices at distancefromand distancefromdepends only on,, and thegraph d...
Word-Representability of Shift Graphs
Content selection saved. Describe the issue below: A graphG=(V,E)G=(V,E)isword-representableif there exists a wordwwover the alphabetVVsuch that lettersxxandyyalternate inwwif and only ifxy∈Exy\in E....
Determined by Spectrum -- from Wolfram MathWorld
Two nonisomorphic graphs can share the samegraph spectrum, i.e., have the same eigenvalues of their adjacency matrices. Such graphs are calledcospectral. For example, thegraph
unionandstar graph, ill...
Cubic Symmetric Graph -- from Wolfram MathWorld
A cubic symmetric graph is asymmetriccubic(i.e., regular of order 3). Such graphs were first studied by Foster (1932). They
have since been the subject of much interest and study. Since cubic graphs ...
Claw-Free Graph -- from Wolfram MathWorld
A graph is claw-freeiffit does not contain thecomplete bipartite graph(known as the "claw graph"; illustrated above)
as aforbidden induced subgraph. Theline graphof any graph is claw-free, as is thec...
Planar Graph -- from Wolfram MathWorld
Agraphis planar if it can be drawn in aplanewithoutgraph edgescrossing (i.e., it hasgraph
crossing number0). The number of planar graphs with, 2, ... nodes are 1, 2, 4, 11, 33, 142, 822, 6966, 79853,...
Nonhamiltonian Graph -- from Wolfram MathWorld
A nonhamiltonian graph is a graph that is notHamiltonian. Alldisconnected graphsare therefore nonhamiltoinian,
as areacylic graphs. Classes of connected graphs that are nonhamiltonian includebarbell ...
Apex Graph -- from Wolfram MathWorld
An apex graph is a graph possessing at least one vertex whose removal results in aplanar graph. The set of vertices whose removal
results in aplanar graphis known as the apices
of the graph. Planar ...
Haar Graph -- from Wolfram MathWorld
A Haar graphis abipartiteregularindexed by apositive integerand obtained by
a simplebinaryencoding of cyclically adjacent vertices.
Haar graphs may beconnectedordisconnected. For example, consider t...
Graphs defined on algebras
There has been a great deal of attention recently to graphs whose vertex set is a group, defined using the group structure. (Thecommuting graph, where
two elements are joined if they commute, is the o...
Position: How can Graphs Help Large Language Models?
Content selection saved. Describe the issue below: With the rapid advancement of large language models (LLMs), classic graph learning tasks have greatly benefited from LLMs, including improved encodin...
Line Graph -- from Wolfram MathWorld
A line graph(also called an adjoint, conjugate, covering, derivative, derived, edge, edge-to-vertex
dual, interchange, representative, or-obrazom graph) of asimple
graphis obtained by associating a ...