Geodesic
On the Boolean function graph of a graph and on its complement
Mathematica Bohemica, Tome 130 (2005) no. 2, pp. 113-134.

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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 $B(G,L(G),\mathop {\mathrm NINC})$ of $G$ is a graph with vertex set $V(G)\cup E(G)$ and two vertices in $B(G,L(G),\mathop {\mathrm NINC})$ 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 $B_1(G)$. In this paper, structural properties of $B_1(G)$ 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.
DOI : 10.21136/MB.2005.134130
Classification : 05C12, 05C15, 05C45, 05C75, 06E30
Keywords: eccentricity; self-centered graph; middle graph; Boolean function graph 
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Janakiraman, T. N.; Muthammai, S.; Bhanumathi, M. On the Boolean function graph of a graph and on its complement. Mathematica Bohemica, Tome 130 (2005) no. 2, pp. 113-134. doi : 10.21136/MB.2005.134130. http://geodesic.mathdoc.fr/articles/10.21136/MB.2005.134130/

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