On (1,2)-domination in cubic graphs

M. H. Fakharan; A. A. Gorzin; Michael A. Henning; A. Jafari; R. Touserkani

doi:10.1016/j.disc.2021.112546

On (1,2)-domination in cubic graphs

M. H. Fakharan, A. A. Gorzin, Michael A. Henning, A. Jafari, R. Touserkani

Mathematics and Applied Mathematics

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

2 Citations (Scopus)

Abstract

A (1,2)-dominating set in a graph G with minimum degree at least 2 is a set S of vertices of G such that every vertex in V(G)∖S has at least one neighbor in S and every vertex in S has at least two neighbors in S. The (1,2)-domination number, γ_1,2(G), of G is the minimum cardinality of a (1,2)-dominating set of G. In this paper we prove that if G is a cubic graph of order n, then [Formula presented], and this bound is tight.

Original language	English
Article number	112546
Journal	Discrete Mathematics
Volume	344
Issue number	10
DOIs	https://doi.org/10.1016/j.disc.2021.112546
Publication status	Published - Oct 2021

Keywords

(r,s)-domination
Cubic graph
Domination

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2021.112546

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title = "On (1,2)-domination in cubic graphs",

abstract = "A (1,2)-dominating set in a graph G with minimum degree at least 2 is a set S of vertices of G such that every vertex in V(G)∖S has at least one neighbor in S and every vertex in S has at least two neighbors in S. The (1,2)-domination number, γ1,2(G), of G is the minimum cardinality of a (1,2)-dominating set of G. In this paper we prove that if G is a cubic graph of order n, then [Formula presented], and this bound is tight.",

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AU - Fakharan, M. H.

AU - Gorzin, A. A.

AU - Henning, Michael A.

AU - Jafari, A.

AU - Touserkani, R.

PY - 2021/10

Y1 - 2021/10

N2 - A (1,2)-dominating set in a graph G with minimum degree at least 2 is a set S of vertices of G such that every vertex in V(G)∖S has at least one neighbor in S and every vertex in S has at least two neighbors in S. The (1,2)-domination number, γ1,2(G), of G is the minimum cardinality of a (1,2)-dominating set of G. In this paper we prove that if G is a cubic graph of order n, then [Formula presented], and this bound is tight.

AB - A (1,2)-dominating set in a graph G with minimum degree at least 2 is a set S of vertices of G such that every vertex in V(G)∖S has at least one neighbor in S and every vertex in S has at least two neighbors in S. The (1,2)-domination number, γ1,2(G), of G is the minimum cardinality of a (1,2)-dominating set of G. In this paper we prove that if G is a cubic graph of order n, then [Formula presented], and this bound is tight.

KW - (r,s)-domination

KW - Cubic graph

KW - Domination

UR - https://www.scopus.com/pages/publications/85110209577

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JO - Discrete Mathematics

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IS - 10

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ER -

On (1,2)-domination in cubic graphs

Abstract

Keywords

ASJC Scopus subject areas

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