Total forcing versus total domination in cubic graphs

Randy Davila; Michael A. Henning

doi:10.1016/j.amc.2019.02.060

Total forcing versus total domination in cubic graphs

Randy Davila, Michael A. Henning

Mathematics and Applied Mathematics

Research output: Contribution to journal › Article › peer-review

12 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 language	English
Pages (from-to)	385-395
Number of pages	11
Journal	Applied Mathematics and Computation
Volume	354
DOIs	https://doi.org/10.1016/j.amc.2019.02.060
Publication status	Published - 1 Aug 2019

Keywords

Cubic graph
Total dominating set
Total forcing set

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2019.02.060

Cite this

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title = "Total forcing versus total domination in cubic graphs",

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).",

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AU - Henning, Michael A.

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N2 - 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).

AB - 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).

KW - Cubic graph

KW - Total dominating set

KW - Total forcing set

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DO - 10.1016/j.amc.2019.02.060

M3 - Article

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VL - 354

SP - 385

EP - 395

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

Total forcing versus total domination in cubic graphs

Abstract

Keywords

ASJC Scopus subject areas

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