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Simple-intersection Graphs of S-acts | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 24 آبان 1404 اصل مقاله (522.83 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.30632.2558 | ||
| نویسندگان | ||
| Xingliang Liang* ؛ Yujie Wang؛ Xiaojie Chen | ||
| Shaanxi University of Science and Technology, Xi’an, Shaanxi 710021, P.R. China | ||
| چکیده | ||
| 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 $GS(S)$. | ||
| کلیدواژهها | ||
| S-act؛ simple-intersection graph؛ clique؛ bipartiteness؛ domination number | ||
| مراجع | ||
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