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 denoted by B1(G). In this paper, we determine domination number, independent, connected, total, cycle, point-set, restrained, split and non-split domination numbers of B1(G) and obtain bounds for the above numbers.
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 denoted by B1(G). In this paper, we determine domination number, independent, connected, total, point-set, restrained, split and non-split domination numbers in the complement B1(G) of B1(G) and obtain bounds for the above numbers.
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. In this paper, global domination number, total global domination number, global point-set domination number and neighborhood number for this graph are obtained.
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 denoted by B1(G). In this paper, structural properties of B1(G) and its complement including traversability and eccentricity properties are studied. In addition, solutions for Boolean function graphs that are total graphs, quasi-total graphs and middle graphs are obtained.