Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 Articles in Press 2025 11 15 Simple-intersection Graphs of S-acts 15044 10.22049/cco.2025.30632.2558 EN Xingliang Liang Shaanxi University of Science and Technology, Xi’an, Shaanxi 710021, P.R. China Yujie Wang Shaanxi University of Science and Technology, Xi’an, Shaanxi 710021, P.R. China Xiaojie Chen Shaanxi University of Science and Technology, Xi’an, Shaanxi 710021, P.R. China Journal Article 2025 05 18 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 $GS(S)$. https://comb-opt.azaruniv.ac.ir/article_15044_093de00a3caf2a5e845f1d901725215c.pdf