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Let m(G) be the cycle rank of a graph G, m^*(G) be the cocycle rank, and the relative complement G-H of a subgraph H of G be defined as that subgraph obtained by deleting the ...

The Goddard-Henning graph, illustrated above in several embeddings, is the 9-node planar graph of graph diameter 2 having domination number gamma=3. It was first constructed ...

In the directed graph above, pick any vertex and follow the arrows in sequence blue-red-red three times. You will finish at the green vertex. Similarly, follow the sequence ...

A graph is called cordial if it is possible to label its vertices with 0s and 1s so that when the edges are labeled with the difference of the labels at their endpoints, the ...

Graphs corresponding to closed walks of length k are known as k-cyclic graphs, or C_k-graphs for short. C_k-graphs are connected by definition. The numbers of C_k-graphs for ...

The adjacency list representation of a graph consists of n lists one for each vertex v_i, 1<=i<=n, which gives the vertices to which v_i is adjacent. The adjacency lists of a ...

An unordered pair representation is a representation of an undirected graph in which edges are specified as unordered pairs of vertex indices. The unordered pairs ...

A graph with minimum vertex degree at least 5 is a line graph iff it does not contain any of the above six graphs, known in this work as Metelsky graphs, as an induced ...

A kayak paddle graph KP(k,m,l) is the graph obtained by joining cycle graphs C_k and C_m by a path of length l (Gallian 2018). KP(3,3,1) is isomorphic to the 3-barbell graph. ...

Let G be a finite, connected, undirected graph with graph diameter d(G) and graph distance d(u,v) between vertices u and v. A radio labeling of a graph G is labeling using ...