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Title: On the Boolean function graph of a graph and on its complement (English)
Author: Janakiraman, T. N.
Author: Muthammai, S.
Author: Bhanumathi, M.
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 130
Issue: 2
Year: 2005
Pages: 113-134
Summary lang: English
Category: math
Summary: 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. (English)
Keyword: eccentricity
Keyword: self-centered graph
Keyword: middle graph
Keyword: Boolean function graph
MSC: 05C12
MSC: 05C15
MSC: 05C45
MSC: 05C75
MSC: 06E30
idZBL: Zbl 1110.05086
idMR: MR2148646
DOI: 10.21136/MB.2005.134130
Date available: 2009-09-24T22:19:10Z
Last updated: 2020-07-29
Stable URL:
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