Domination numbers on the complement of the Boolean function graph of a graph

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

Mathematica Bohemica (2005)

  • Volume: 130, Issue: 3, page 247-263
  • 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, we determine domination number, independent, connected, total, point-set, restrained, split and non-split domination numbers in the complement B ¯ 1 ( G ) of B 1 ( G ) and obtain bounds for the above numbers.

How to cite

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Janakiraman, T. N., Muthammai, S., and Bhanumathi, M.. "Domination numbers on the complement of the Boolean function graph of a graph." Mathematica Bohemica 130.3 (2005): 247-263. <http://eudml.org/doc/249591>.

@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, we determine domination number, independent, connected, total, point-set, restrained, split and non-split domination numbers in the complement $\bar\{B\}_\{1\}(G)$ of $B_\{1\}(G)$ and obtain bounds for the above numbers.},
author = {Janakiraman, T. N., Muthammai, S., Bhanumathi, M.},
journal = {Mathematica Bohemica},
keywords = {domination number; eccentricity; radius; diameter; neighborhood; perfect matching; Boolean function graph; eccentricity; radius; diameter; neighborhood; perfect matching},
language = {eng},
number = {3},
pages = {247-263},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Domination numbers on the complement of the Boolean function graph of a graph},
url = {http://eudml.org/doc/249591},
volume = {130},
year = {2005},
}

TY - JOUR
AU - Janakiraman, T. N.
AU - Muthammai, S.
AU - Bhanumathi, M.
TI - Domination numbers on the complement of the Boolean function graph of a graph
JO - Mathematica Bohemica
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 130
IS - 3
SP - 247
EP - 263
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, we determine domination number, independent, connected, total, point-set, restrained, split and non-split domination numbers in the complement $\bar{B}_{1}(G)$ of $B_{1}(G)$ and obtain bounds for the above numbers.
LA - eng
KW - domination number; eccentricity; radius; diameter; neighborhood; perfect matching; Boolean function graph; eccentricity; radius; diameter; neighborhood; perfect matching
UR - http://eudml.org/doc/249591
ER -

References

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