IJPAM: Volume 81, No. 2 (2012)

AN IDEAL-BASED ZERO DIVISOR GRAPH
OF PO-$\Gamma$-SEMIGROUPS

B. Elavarasan
Department of Mathematics
School of Science and Humanities
Karunya University,
Coimbatore, 641 114, Tamilnadu, INDIA


Abstract. In this paper, we study the notion of ideal-based zero-divisor graph structure of po-$\Gamma$-semigroup $M $ with respect to reflexive ideal $I$ of $M,$ denoted by $\Gamma_{I}(M),$ whose vertices are the set $\{x\in M\backslash I: $ there exists $y\in M\backslash I $ such that $x\Gamma y\subseteq I \}$ with distinct vertices $x$ and $y$ are adjacent if and only if $x\Gamma y\subseteq I.$ We investigate the interplay between the po-$\Gamma$-semigroups properties of $M $ and the graph-theoretic properties of $\Gamma_{I}(M).$

Received: June 17, 2012

AMS Subject Classification: 03G25, 06F35, 05C99, 06B35

Key Words and Phrases: ideal, graph, diameter, cycle, bipartite graph

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 81
Issue: 2