A Note on a Line Graph of the Zero Divisor Graph of a Commutative Ring


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Authors

  • Jaydeep Parejiya Department of Mathematics, Government Polytechnic, Rajkot, Gujarat, India
  • Yesha Hathi Department of Mathematics, Government Polytechnic, Rajkot, Gujarat, India
  • Patat Sarman Department of Mathematics, Government Polytechnic, Rajkot, Gujarat, India

Keywords:

Line graph, zero divisor graph, diameter of a graph

Abstract

The rings considered in this article are commutative with identity $ 1 \neq 0 $. Recall that the zero divisor graph of a ring $ R $ is a simple undirected graph whose vertex set is the set of all nonzero zero divisors of the ring $ R $ and two distinct vertices $ x, y $ are adjacent in this graph if and only if $xy = 0$. In this article we studied the line graph of the zero divisor graph of a ring and we proved some results regarding the diameter of the line graph.

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Published

15-03-2020

How to Cite

Jaydeep Parejiya, Yesha Hathi, & Patat Sarman. (2020). A Note on a Line Graph of the Zero Divisor Graph of a Commutative Ring. International Journal of Mathematics And Its Applications, 8(1), 49–53. Retrieved from http://ijmaa.in/index.php/ijmaa/article/view/174

Issue

Section

Research Article