Zero forcing versus domination in cubic graphs

Randy Davila, Michael A. Henning

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

In this paper, we study a dynamic coloring of the vertices of a graph G that starts with an initial subset S of colored vertices, with all remaining vertices being non-colored. At each discrete time interval, a colored vertex with exactly one non-colored neighbor forces this non-colored neighbor to be colored. The initial set S is a zero forcing set of G if, by iteratively5 applying the forcing process, every vertex in G becomes colored. The zero forcing number of G is the minimum cardinality of a zero forcing set of G. In this paper, we prove that if G≠ K4 is a connected cubic graph, then the zero forcing number of G is bounded above by twice its domination number, where the domination number of G is the minimum cardinality of a set of vertices of G such that every vertex not in S is adjacent to some vertex in S.

Original languageEnglish
Pages (from-to)553-577
Number of pages25
JournalJournal of Combinatorial Optimization
Volume41
Issue number2
DOIs
Publication statusPublished - Feb 2021

Keywords

  • Dominating set
  • Domination number
  • Zero forcing number
  • Zero forcing set

ASJC Scopus subject areas

  • Computer Science Applications
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Theory and Mathematics
  • Applied Mathematics

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