Amirkabir University of Technology AUT Journal of Mathematics and Computing 2783-2449 6 2 2025 02 01 Dynamic monopolies in simple graphs 151 162 5350 10.22060/ajmc.2024.22585.1178 EN Leila Musavizadeh Jazaeri Department of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Razavi Khorasan, Iran Leila Sharifan Department of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Razavi Khorasan, Iran Journal Article 2023 07 27 This paper studies a repetitive polling game played on an n-vertex graph G. At first, each vertex is colored, Black or White. At each round, each vertex (simultaneously) recolors itself by the color of the majority of its closed neighborhood. The variants of the model differ in the choice of a particular tiebreaking rule. We assume the tie-breaking rule is Prefer-White and we study the relation between the notion of “dynamic monopoly” and “vertex cover” of G. In particular, we show that any vertex cover of G is a dynamic monopoly or reaches a 2−periodic coloring. Moreover, we compute dyn(G) for some special classes of graphs including paths, cycles and links of some graphs. https://ajmc.aut.ac.ir/article_5350_b11efa85edab3270414a3b253100f18d.pdf