Simple-intersection Graphs of S-acts

Articles in Press

Document Type : Original paper

Authors

Shaanxi University of Science and Technology, Xi’an, Shaanxi 710021, P.R. China

Abstract

The intersection graph of an algebraic structure plays a pivotal role in understanding and analyzing algebraic structures---such as groups, rings, modules, acts---by encoding substructural relationships into graph-theoretic frameworks. In this paper, we introduce a new intersection-graph type for an $S$-act $A$ over a semigroup $S$, termed the \emph{simple intersection graph} of $A$, denoted by $GS(A)$. We focus on the relationship between algebraic properties of $A$ and graph-theoretic characteristics of $GS(A)$, including degree, cycles, cliques, connectivity, bipartiteness and dominaning sets. Specifically, we characterize $S$-acts $A$ for which $GS(A)$ is complete, connected or complete bipartite, and determine key invariants such as degree, girth, diameter, clique number and domination number of $GS(A)$. Applications include solutions to coloring optimization problems and extensions to semigroup-based graphs $GS(S)$.

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References

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Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 15 November 2025

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