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arXiv · 1911.00144

On the Total Graph of a Finite Commutative Ring

Mohammad Hadi Shekarriz·Mohammad Hasan Shirdareh Haghighi·Habib Sharif
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Abstract

Let $R$ be a finite commutative ring with $1\ne 0$. In this article, we study the total graph of $R$, denoted by $τ(R)$, determine some of its basic graph-theoretical properties, determine when it is Eulerian, and find some conditions under which this graph is isomorphic to $Cay(R,Z(R)\backslash\lbrace 0\rbrace)$. We shall also compute the domination number of $τ(R).

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Mohammad Hadi Shekarriz, Mohammad Hasan Shirdareh Haghighi, Habib Sharif. 2019-10-31. On the Total Graph of a Finite Commutative Ring. https://doi.org/10.1080/00927872.2011.585680

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