A generalization of total graphs of modules
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 $\Gamma_{N^{\star}}(M)$ denote the (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 $\Gamma_{N^{\star}}(M)$ and investigate the independence number and chromatic number.
Keywords:
Commutative ring, total graph,
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- ISSN: 1306-6048
- Yayın Aralığı: Yılda 2 Sayı
- Başlangıç: 2007
- Yayıncı: Abdullah HARMANCI