November 8, 2025

On Cayley Sum Graph of Ideals of a Ring

Key Points

Cayley sum graphs exhibit unique properties in defining structural characteristics of rings and their ideals.
Analysis reveals important metrics like clique number and perfectness in these mathematical structures.
Study utilizes theoretical models to classify rings based on characteristics of their Cayley sum graphs.
Findings support broader applications of algebraic structures in mathematics, enhancing understanding of ideal relationships.

Abstract

Let Formula: see text be a commutative ring with unity, Formula: see text be the set of all ideals of Formula: see text and Formula: see text be a subset of Formula: see text. Cayley sum graph of ideals of Formula: see text, denoted by Formula: see text, is a simple undirected graph with vertex set Formula: see text and two distinct vertices Formula: see text and Formula: see text are adjacent (Formula: see text), whenever Formula: see text or Formula: see text, for some ideal Formula: see text in Formula: see text. In this paper, we determine the girth, chromatic number, clique number, perfect code, and perfectness of the Cayley sum graphs Formula: see text and Formula: see text (where Formula: see text denotes the set of all non-zero maximal ideals of Formula: see text). Finally, we classify the family of rings whose Cayley sum graphs are split, co-graph, threshold, chordal and claw-free.

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Cite This Study

Roy et al. (Fri,) studied this question.

synapsesocial.com/papers/690e8b6ca5b062d7a4e7353c https://doi.org/https://doi.org/10.1142/s0219498827500782

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