On the Boolean function graph of a graph and on its complement

On the Boolean Function Graph of a Graph and on Its Complement

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...

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Domination Numbers on the Complement of the Boolean Function Graph of a Graph

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...

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On the Connectivity of a Graph and its Complement Graph

In this paper, we study the connectivity of the complement of a graph. We first establish a simple formula to compute the connectivity of a graph that comes from the join of graphs. Base on this formula, we give an upper and a lower bound to the connectivity of the complement of a graph. Keyword: connectivity, complement, join, vertex of attachment.

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Domination Numbers on the Boolean Function Graph of a Graph

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...

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SOME RESULTS ON THE COMPLEMENT OF THE INTERSECTION GRAPH OF SUBGROUPS OF A FINITE GROUP

Let G be a group. Recall that the intersection graph of subgroups of G is an undirected graph whose vertex set is the set of all nontrivial subgroups of G and distinct vertices H,K are joined by an edge in this graph if and only if the intersection of H and K is nontrivial. The aim of this article is to investigate the interplay between the group-theoretic properties of a finite group G and the...

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On the Boolean function graph of a graph and on its complement

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