Bikash Barman and Kukil Kalpa Rajkhowa
The authors study the interdisciplinary relation between graph and algebraic structure ring defining a new graph, namely “non-essential sum graph”. The nonessential sum graph…
Abstract
Purpose
The authors study the interdisciplinary relation between graph and algebraic structure ring defining a new graph, namely “non-essential sum graph”. The nonessential sum graph, denoted by NES(R), of a commutative ring R with unity is an undirected graph whose vertex set is the collection of all nonessential ideals of R and any two vertices are adjacent if and only if their sum is also a nonessential ideal of R.
Design/methodology/approach
The method is theoretical.
Findings
The authors obtain some properties of NES(R) related with connectedness, diameter, girth, completeness, cut vertex, r-partition and regular character. The clique number, independence number and domination number of NES(R) are also found.
Originality/value
The paper is original.