An Ideal-Based Dot Total Graph of a Commutative Ring

Mohammad Ashraf, Jaber H. Asalool, Abdulaziz M. Alanazi and Ahmed Alamer
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Mohammad Ashraf: Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
Jaber H. Asalool: Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
Abdulaziz M. Alanazi: Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia
Ahmed Alamer: Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia

Mathematics, 2021, vol. 9, issue 23, 1-13

Abstract: In this paper, we introduce and investigate an ideal-based dot total graph of commutative ring R with nonzero unity. We show that this graph is connected and has a small diameter of at most two. Furthermore, its vertex set is divided into three disjoint subsets of R . After that, connectivity, clique number, and girth have also been studied. Finally, we determine the cases when it is Eulerian, Hamiltonian, and contains a Eulerian trail.

Keywords: commutative rings; zero-divisor graph; dot total graph; ideal-based; zero-divisors (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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