On Eulerianity and Hamiltonicity in Annihilating-ideal Graphs

Author(s):

A. Kourehpaz , R. Nikandish*

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:

Let $R$ be a commutative ring with identity, and $ mathrm{A}(R) $ be the set of ideals with non-zero annihilator. The annihilating-ideal graph of $ R $ is defined as the graph $AG(R)$ with the vertex set $ mathrm{A}(R)^{*}=mathrm{A}(R)setminuslbrace 0rbrace $ and two distinct vertices $ I $ and $ J $ are adjacent if and only if $ IJ=0 $. In this paper, conditions under which $AG(R)$ is either Eulerian or Hamiltonian are given.

Keywords:

Annihilating-ideal graph , Eulerian graphs , Hamiltonian graphs

Language:
English
Published:
Iranian Journal of Mathematical Sciences and Informatics, Volume:16 Issue: 1, May 2021
Pages:
97 to 104
https://www.magiran.com/p2262243