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For any graph $G$, let $V\left(G\right)$ and $E\left(G\right)$ denote the vertex set and the edge set of $G$ respectively. The Boolean function graph $B(G,L(G),\mathrm{N}INC)$ of $G$ is a graph with vertex set $V\left(G\right)\cup E\left(G\right)$ and two vertices in $B(G,L(G),\mathrm{N}INC)$ 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 $V\left(G\right)$ and $E\left(G\right)$ denote the vertex set and the edge set of $G$ respectively. The Boolean function graph $B(G,L(G),\mathrm{N}INC)$ of $G$ is a graph with vertex set $V\left(G\right)\cup E\left(G\right)$ and two vertices in $B(G,L(G),\mathrm{N}INC)$ 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 $B_1\left(G\right)$. In this paper, we determine domination number, independent, connected, total, cycle, point-set, restrained, split and non-split domination...

For any graph $G$, let $V\left(G\right)$ and $E\left(G\right)$ denote the vertex set and the edge set of $G$ respectively. The Boolean function graph $B(G,L(G),\mathrm{N}INC)$ of $G$ is a graph with vertex set $V\left(G\right)\cup E\left(G\right)$ and two vertices in $B(G,L(G),\mathrm{N}INC)$ 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 $B_1\left(G\right)$. In this paper, we determine domination number, independent, connected, total, point-set, restrained, split and non-split domination numbers...

For any graph $G$, let $V\left(G\right)$ and $E\left(G\right)$ denote the vertex set and the edge set of $G$ respectively. The Boolean function graph $B(G,L(G),\mathrm{N}INC)$ of $G$ is a graph with vertex set $V\left(G\right)\cup E\left(G\right)$ and two vertices in $B(G,L(G),\mathrm{N}INC)$ 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 $B_1\left(G\right)$. In this paper, structural properties of $B_1\left(G\right)$ and its complement including traversability and eccentricity properties are studied. In addition,...