A generalization of total graphs of modules

Authors : Ahmad ABBASİ, Leila Hamidian JAHROMİ

Pages : 28-38

Doi:10.24330/ieja.325918

View : 60 | Download : 12

Publication Date : 2017-07-11

Article Type : Research Paper

Abstract :Let $R$ be a commutative ring, and let $M\neq 0$ be an $R$-module with a non-zero proper submodule $N$, where $N^{\star}=N-\{0\}$.  Let $\Gamma_{N^{\star}}insert ignore into journalissuearticles values(M);$ denote the insert ignore into journalissuearticles values(undirected); simple graph  with vertices $ \{x \in  M -N\,|\,x+x^\prime \in N^{\star}$ for some $x\neq x` \in M-N \}$, where distinct vertices $x$ and $y$ are adjacent if and only if  $x+y \in N^{\star}$. We determine some graph theoretic properties of $\Gamma_{N^{\star}}insert ignore into journalissuearticles values(M);$ and investigate  the  independence number and chromatic number.  
Keywords : Commutative ring, total graph

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