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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 ...

The Balaban 11-cage is the unique 11-cage graph, derived via a tree excision from the 12-cage graph by Balaban (1973) and proven unique by McKay and Myrvold in 2003. It is ...

A search algorithm of a graph which explores all nodes adjacent to the current node before moving on. For cyclic graphs, care must be taken to make sure that no nodes are ...

For a graph G and a subset S of the vertex set V(G), denote by N_G[S] the set of vertices in G which are in S or adjacent to a vertex in S. If N_G[S]=V(G), then S is said to ...

The Klein bottle crossing number of a graph G is the minimum number of crossings possible when embedding G on a Klein bottle (cf. Garnder 1986, pp. 137-138). While the ...

An independent edge set, also called a matching, of a graph G is a subset of the edges such that no two edges in the subset share a vertex in G. A maximum independent edge ...

A search algorithm of a tree that explores the first child of a node before visiting its siblings. Tarjan (1972) and Hopcroft and Tarjan (1973) showed that depth-first search ...

Bonato et al. (2014, 2015) defined the burning number of a simple graph as follows. Consider a process called burning involving are discrete time steps. Each node is either ...

An analog of the polyominoes and polyiamonds in which collections of regular hexagons are arranged with adjacent sides. They are also called hexes, hexas, or polyfrobs ...

The vertex connectivity kappa(G) of a graph G, also called "point connectivity" or simply "connectivity," is the minimum size of a vertex cut, i.e., a vertex subset S subset= ...