P4-Decomposition in Boolean function graph of B3(G)

Abstract

For any graph $G$, let $V(G)$ and $E(G)$ denote the vertex set and edge set of $G$ respectively. The Boolean function graph $B(\overline{K p}, \overline{L(G)}, N I N C)$ of $G$ is a graph with vertex set $V(G) \cup E(G)$ and two vertices in $B(\overline{K p}, \overline{L(G)}, N I N C)$ are adjacent if and only if they correspond to two non adjacent edges of $G$ or to a vertex and an edge not incident to it in $G$. For brevity, this graph is denoted by $B_3(G)$. In this paper, $P_4$ - decomposition in Boolean Function Graph $B(\overline{K p}, \overline{L(G)}, \mathrm{NINC})$ of some standard graphs and corona graphs are obtained.