MATHEMATICA BOHEMICA, Vol. 130, No. 2, pp. 113-134 (2005)

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

T. N. Janakiraman, S. Muthammai, M. Bhanumathi

T. N. Janakiraman, National Institute of Technology, Tiruchirappalli, 620 015, India, e-mail:; S. Muthammai, M. Bhanumathi, Government Arts College for Women, Pudukkottai, 622 001, India

Abstract: 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 $V(G)\cup E(G)$ 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 $B_1(G)$. 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.

Keywords: eccentricity, self-centered graph, middle graph, Boolean function graph

Classification (MSC2000): 05C15

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