Dynamic monopolies in simple graphs
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 p...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Amirkabir University of Technology
2025-02-01
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| Series: | AUT Journal of Mathematics and Computing |
| Subjects: | |
| Online Access: | https://ajmc.aut.ac.ir/article_5350_2bb6c5d854497148d55a2f5aeaa8486f.pdf |
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| Summary: | 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 tie-breaking 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 ${\rm{dyn}}(G)$ for some special classes of graphs including{ paths, cycles and links of some graphs}. |
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| ISSN: | 2783-2449 2783-2287 |