Total forcing versus total domination in cubic graphs

Randy Davila and Michael A. Henning

Applied Mathematics and Computation, 2019, vol. 354, issue C, 385-395

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, γt(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 Ft(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 K3,3, then Ft(G)≤32γt(G).

Keywords: Total forcing set; Total dominating set; Cubic graph (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:354:y:2019:i:c:p:385-395

DOI: 10.1016/j.amc.2019.02.060

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