@article{Alzubaidi2026, 
author = {Husniyah Alzubaidi},
title = {On the P-intersection graphs of acts over semigroups: applications to connectivity and monophonic convexity with clique structure},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {7},
pages = {20619-20644},
keywords = {semigroup action, topological semigroup, intersection graph, clique number, monophonic path},
url = {https://www.sciopen.com/article/10.3934/math.2026839},
doi = {10.3934/math.2026839},
abstract = {In this paper, we present the    Ψ-intersection graph        Ψ                  S              (      B    ) associated with an    S-act over topological semigroups. We investigate how the internal structure of    S-acts, particularly the presence and distribution of simple subacts, determines fundamental graph-theoretic properties of        Ψ                  S              (      B    ). Characterizations of connectivity, bipartiteness, girth, and diameter are established in terms of decomposition properties and chain conditions on subacts. We further analyze the clique structure of        Ψ                  S              (      B    ), showing that every clique contains at most one simple subact and describing maximal cliques through families of non-simple subacts intersecting via simple components. Domination-type parameters are also studied by introducing indecomposable controlling sets and deriving bounds for the control number of        Ψ                  S              (      B    ). Finally, by using monophonic convexity and the    m-topology on graphs, we examine induced path structures and their interaction with algebraic paths in    S-acts, revealing connections between geodesic behavior and semigroup actions. These results provide a unified algebraic, topological, and graph-theoretic framework and open new combinatorial and metric approaches to the study of topological path semigroups.}
}