For any graph G, let V (G) and E(G) denote the vertex set and the edge set of G respectively. The Boolean function graph B(G, L(G),NINC) of G is a graph with vertex set V (G) ∪ E(G) and two vertices in B(G, L(G),NINC) are adjacent if and only if they correspond to two adjacent vertices of G, two adjacent edges of G or to a vertex and an edge not incident to it in G. For brevity, this graph is d...

For any graph G, let V (G) and E(G) denote the vertex set and the edge set of G respectively. The Boolean function graph B(G, L(G),NINC) of G is a graph with vertex set V (G) ∪ E(G) and two vertices in B(G, L(G),NINC) are adjacent if and only if they correspond to two adjacent vertices of G, two adjacent edges of G or to a vertex and an edge not incident to it in G. For brevity, this graph is d...

The existence of a constant time algorithm for solving different domination problems on the subclass of polygraphs, rotagraphs and fasciagraphs, is shown by means of path algebras. As these graphs include products (the Cartesian, strong, direct, lexicographic) of paths and cycles, we implement the algorithm to get formulas in the case of the domination numbers, the Roman domination numbers and ...

A set S of vertices in graph [Formula: see text] is a [Formula: see text], abbreviated TRDS, of G if every vertex of G is adjacent to a vertex in S and every vertex of [Formula: see text] is adjacent to a vertex in [Formula: see text]. The [Formula: see text] of G, denoted by [Formula: see text], is the minimum cardinality of a TRDS of G. Jiang and Kang (J Comb Optim. 19:60-68, 2010) characteri...