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The (n,k)-arrangement graph A_(n,k) is defined as the graph on the vertex set consisting of the permutations of {1,2,...,n} containing at most k elements where vertices are ...

A graph is strongly perfect if every induced subgraph H has an independent vertex set meeting all maximal cliques of H (Berge and Duchet 1984, Ravindra 1999). Every strongly ...

A biplanar graph is defined as a graph that is the graph union of two planar edge-induced subgraphs. In other words, biplanar graphs are graphs with graph thickness 1 or 2 ...

A traceable graph is a graph that possesses a Hamiltonian path. Hamiltonian graphs are therefore traceable, but the converse is not necessarily true. Graphs that are not ...

The Zara graph is the unique graph on 126 vertices satisfying the properties that 1) every maximal clique (of which there are a total of 567) has six vertices, and 2) that if ...

The periphery of a graph G is the subgraph of G induced by vertices that have graph eccentricities equal to the graph diameter. The periphery of a connected graph may be ...

A uniquely Hamiltonian graph is a graph possessing a single Hamiltonian cycle. Classes of uniquely Hamiltonian graphs include the cycle graphs C_n, Hanoi graphs H_n, ladder ...

A k×m×n hexagonal grid graph is a graph of adjoined hexagons consisting of k hexagons along the horizontal triangular axis, m along the northeast axis, and n along the ...

Define an antipode of a given graph vertex v_i as a vertex v_j at greatest possible graph distance from v_i. Then an antipodal graph is a connected graph in which each vertex ...

A bridged graph is a graph that contains one or more graph bridges. Examples of bridged graphs include path graphs, ladder rung graphs, the bull graph, star graphs, and ...