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A connected graph is graph that is connected in the sense of a topological space, i.e., there is a path from any point to any other point in the graph. A graph that is not ...

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 ...

A cycle of a graph G, also called a circuit if the first vertex is not specified, is a subset of the edge set of G that forms a path such that the first node of the path ...

A graph G is a hypotraceable graph if G has no Hamiltonian path (i.e., it is not a traceable graph), but G-v has a Hamiltonian path (i.e., is a traceable graph) for every v ...

An untraceable graph is a graph that does not possess a Hamiltonian path, i.e., one that is not traceable. All disconnected graphs are therefore untraceable. Untraceable ...

Ball and Coxeter (1987, pp. 277-278) define the ladder graph nP_2, here called the ladder rung graph, of order n as the graph union of n copies of the path graph P_2. The ...

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 ...

The m-book graph is defined as the graph Cartesian product B_m=S_(m+1) square P_2, where S_m is a star graph and P_2 is the path graph on two nodes. The generalization of the ...

The (m,n)-tadpole graph, also called a dragon graph (Truszczyński 1984) or kite graph (Kim and Park 2006), is the graph obtained by joining a cycle graph C_m to a path graph ...

A fan graph F_(m,n) is defined as the graph join K^__m+P_n, where K^__m is the empty graph on m nodes and P_n is the path graph on n nodes. The case m=1 corresponds to the ...