A characterization of rings whose unitary Cayley graphs are planar-Reference-Cited by-同舟云学术

A characterization of rings whose unitary Cayley graphs are planar

Published:2018-08-23 Issue:09 Volume:17 Page:1850178
ISSN:0219-4988
Container-title:Journal of Algebra and Its Applications
language:en
Short-container-title:J. Algebra Appl.

Author:

Su Huadong¹,Zhou Yiqiang²

Affiliation:

1. School of Mathematical and Statistics Sciences, Guangxi Teachers Education University, Nanning, Guangxi 530023, P. R. China

2. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL A1C 5S7, Canada

Abstract

Let [Formula: see text] be a ring with identity. The unitary Cayley graph of [Formula: see text] is the simple graph with vertex set [Formula: see text], where two distinct vertices [Formula: see text] and [Formula: see text] are linked by an edge if and only if [Formula: see text] is a unit of [Formula: see text]. A graph is said to be planar if it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In this paper, we completely characterize the rings whose unitary Cayley graphs are planar.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219498818501785

Reference26 articles.

1. On the Unitary Cayley Graph of a Finite Ring

2. When a zero-divisor graph is planar or a complete r-partite graph

3. On the genus of generalized unit and unitary Cayley graphs of a commutative ring

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5. Counting pure k cycles in sequences of Cayley graphs

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