Weakly Perfect Graphs of Modules

Document Type : بنیادی - نظری

Authors

1 Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395-3697 Tehran, Iran

2 Department of Mathematics University of Mazandaran Babolsar, Iran

3 Department of Mathematics, Payame Noor University (PNU) Tehran, Iran

10.30473/coam.2021.55089.1149

Abstract

In this study‎, ‎$R$ and $M$ are assumed to be a commutative ring with non-zero identity $M$ and an $R$-module‎, ‎respectively‎. ‎Scalar Product Graph of $M$‎, ‎denoted by $G_R(M)$‎, ‎is a graph with the vertex-set $M$ and two different vertices $a$ and $b$ in $M$ are connected if and only if there exists $r$ belong to $R$ such that $a=rb$ or $b=ra$‎. ‎This paper studies some properties of such weakly perfect graphs‎.

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