Total forcing versus total domination in cubic graphs

Randy Davila, Michael A. Henning

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

A set S of vertices in a graph G is a total dominating set of G if every vertex has a neighbor in S. The total domination number, γ t (G), is the minimum cardinality of a total dominating set of G. A total forcing set in a graph G is a forcing set (zero forcing set) in G which induces a subgraph without isolated vertices. The total forcing number of G, denoted F t (G), is the minimum cardinality of a total forcing set in G. Our main contribution is to show that the total forcing number and the total domination number of a cubic graph are related. More precisely, we prove that if G is a connected cubic graph different from K 3,3 , then F t (G)≤[Formula presented]γ t (G).

Original languageEnglish
Pages (from-to)385-395
Number of pages11
JournalApplied Mathematics and Computation
Volume354
DOIs
Publication statusPublished - 1 Aug 2019

Keywords

  • Cubic graph
  • Total dominating set
  • Total forcing set

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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