Structural Properties of Absorption Cayley Graphs

Authors

Deepa Sinha, Department of Mathematics, South Asian University, Akbar Bhawan Chanakyapuri, New Delhi-110021, India.Follow
Deepakshi Sharma, Department of Mathematics, South Asian University, Akbar Bhawan Chanakyapuri, New Delhi-110021, India.Follow

Author Country (or Countries)

India.

Abstract

Let R be a commutative ring with two binary operators addition (+) and multiplication (.). Then Zn is a ring of integers modulo n, where n is a positive integer. An Absorption Cayley graph denoted by W(Zn) is a graph whose vertex set is Zn, the integer modulo n and edge set E = {ab : a+b ∈ S}, where S = {a ∈ Zn : ab = ba = a for some b ∈ Zn,b 6= a}. Here ab = a is the Absorption property as b is absorbed in a. We study the characterization of Absorption cayley graphs along with its properties such as connectedness, degree, hamiltoniacity, diameter, planarity, girth, regularity etc.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/100626

Recommended Citation

Sinha, Deepa and Sharma, Deepakshi (2016) "Structural Properties of Absorption Cayley Graphs," Applied Mathematics & Information Sciences: Vol. 10: Iss. 6, Article 26.
DOI: http://dx.doi.org/10.18576/amis/100626
Available at: https://digitalcommons.aaru.edu.jo/amis/vol10/iss6/26