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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. ...

An edge subdivision is the insertion of a new vertex v_j in the middle of an exiting edge e=v_iv_k accompanied by the joining of the original edge endpoints with the new ...

A connected bipartite graph is called Hamilton-laceable, a term apparently introduced in Simmons (1978), if it has a u-v Hamiltonian path for all pairs of vertices u and v, ...

The snub dodecahedral graph is a quintic graph on 60 nodes and 150 edges that corresponds to the skeleton of the snub dodecahedron, great inverted snub icosidodecahedron, ...

Let the vertices of a graph G be numbered with distinct integers 1 to |G|. Then the dilation of G is the maximum (absolute) difference between integers assigned to adjacent ...

A simple unlabeled graph whose connectivity is considered purely on the basis of topological equivalence, so that two edges (v_1,v_2) and (v_2,v_3) joined by a node v_2 of ...

A path in a graph G is a subgraph of G that is a path graph (West 2000, p. 20). The length of a path is the number of edges it contains. In most contexts, a path must contain ...

The Robertson-Wegner graph is of the four (5,5)-cage graphs, also called Robertson's cage (Read and Wilson 1998, p. 273). Like the other (5,5)-cages, the Robertson-Wegner ...

An extremal graph in which the forced triangles are all the same color. Call R the number of red monochromatic forced triangles and B the number of blue monochromatic forced ...

The study of how the intrinsic structure of graphs ensures certain types of properties (e.g., clique-formation and graph colorings) under appropriate conditions.