Quotient Energy of Zero Divisor Graphs And Identity Graphs

Abstract

Consider the (p,q) simple connected graph . The sum absolute values of the spectrum of quotient matrix of a graph make up the graph's quotient energy. The objective of this study is to examine the quotient energy of identity graphs and zero-divisor graphs of commutative rings using group theory, graph theory, and applications. In this study, the identity graphs derived from the group and a few classes of zero-divisor graphs of the commutative ring R are examined.

Keywords

• Commutative ring, Identity Graphs, Quotient energy, Quotient matrix, Zero-Divisor Graphs