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

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

Mathematica Bohemica (2005)

  • Volume: 130, Issue: 2, page 113-134
  • ISSN: 0862-7959

Abstract

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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 ) , N I N C ) of G is a graph with vertex set V ( G ) ∪ E ( G ) and two vertices in B ( G , L ( G ) , N I N C ) 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.

How to cite

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Janakiraman, T. N., Muthammai, S., and Bhanumathi, M.. "On the Boolean function graph of a graph and on its complement." Mathematica Bohemica 130.2 (2005): 113-134. <http://eudml.org/doc/249575>.

@article{Janakiraman2005,
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 $B(G,L(G),\mathop \{\mathrm \{N\}INC\})$ of $G$ is a graph with vertex set $V(G)\cup E(G)$ and two vertices in $B(G,L(G),\mathop \{\mathrm \{N\}INC\})$ 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 $B_1(G)$. 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.},
author = {Janakiraman, T. N., Muthammai, S., Bhanumathi, M.},
journal = {Mathematica Bohemica},
keywords = {eccentricity; self-centered graph; middle graph; Boolean function graph; eccentricity; self-centered graph; middle graph},
language = {eng},
number = {2},
pages = {113-134},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the Boolean function graph of a graph and on its complement},
url = {http://eudml.org/doc/249575},
volume = {130},
year = {2005},
}

TY - JOUR
AU - Janakiraman, T. N.
AU - Muthammai, S.
AU - Bhanumathi, M.
TI - On the Boolean function graph of a graph and on its complement
JO - Mathematica Bohemica
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 130
IS - 2
SP - 113
EP - 134
AB - 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 $B(G,L(G),\mathop {\mathrm {N}INC})$ of $G$ is a graph with vertex set $V(G)\cup E(G)$ and two vertices in $B(G,L(G),\mathop {\mathrm {N}INC})$ 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 $B_1(G)$. 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.
LA - eng
KW - eccentricity; self-centered graph; middle graph; Boolean function graph; eccentricity; self-centered graph; middle graph
UR - http://eudml.org/doc/249575
ER -

References

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  7. The neighborhood number of a graph, Indian J. Pure Appl. Math. 16 (1985), 126–132. (1985) MR0780299
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  9. 10.2307/2371086, Am. J. Math. 54 (1932), 150–168. (1932) Zbl0003.32804MR1506881DOI10.2307/2371086

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