Perfect Roman domination in trees

Michael A. Henning; William F. Klostermeyer; Gary MacGillivray

doi:10.1016/j.dam.2017.10.027

Perfect Roman domination in trees

Michael A. Henning, William F. Klostermeyer, Gary MacGillivray

Mathematics and Applied Mathematics

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

38 Citations (Scopus)

Abstract

A perfect Roman dominating function on a graph G is a function f:V(G)→{0,1,2} satisfying the condition that every vertex u with f(u)=0 is adjacent to exactly one vertex v for which f(v)=2. The weight of a perfect Roman dominating function f is the sum of the weights of the vertices. The perfect Roman domination number of G, denoted γ_R^p(G), is the minimum weight of a perfect Roman dominating function in G. We show that if G is a tree on n≥3 vertices, then γ_R^p(G)≤[Formula presented]n, and we characterize the trees achieving equality in this bound.

Original language	English
Pages (from-to)	235-245
Number of pages	11
Journal	Discrete Applied Mathematics
Volume	236
DOIs	https://doi.org/10.1016/j.dam.2017.10.027
Publication status	Published - 19 Feb 2018

Keywords

Dominating set
Perfect dominating set
Roman dominating function
Tree

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/j.dam.2017.10.027

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title = "Perfect Roman domination in trees",

abstract = "A perfect Roman dominating function on a graph G is a function f:V(G)→{0,1,2} satisfying the condition that every vertex u with f(u)=0 is adjacent to exactly one vertex v for which f(v)=2. The weight of a perfect Roman dominating function f is the sum of the weights of the vertices. The perfect Roman domination number of G, denoted γRp(G), is the minimum weight of a perfect Roman dominating function in G. We show that if G is a tree on n≥3 vertices, then γRp(G)≤[Formula presented]n, and we characterize the trees achieving equality in this bound.",

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AU - Klostermeyer, William F.

AU - MacGillivray, Gary

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N2 - A perfect Roman dominating function on a graph G is a function f:V(G)→{0,1,2} satisfying the condition that every vertex u with f(u)=0 is adjacent to exactly one vertex v for which f(v)=2. The weight of a perfect Roman dominating function f is the sum of the weights of the vertices. The perfect Roman domination number of G, denoted γRp(G), is the minimum weight of a perfect Roman dominating function in G. We show that if G is a tree on n≥3 vertices, then γRp(G)≤[Formula presented]n, and we characterize the trees achieving equality in this bound.

AB - A perfect Roman dominating function on a graph G is a function f:V(G)→{0,1,2} satisfying the condition that every vertex u with f(u)=0 is adjacent to exactly one vertex v for which f(v)=2. The weight of a perfect Roman dominating function f is the sum of the weights of the vertices. The perfect Roman domination number of G, denoted γRp(G), is the minimum weight of a perfect Roman dominating function in G. We show that if G is a tree on n≥3 vertices, then γRp(G)≤[Formula presented]n, and we characterize the trees achieving equality in this bound.

KW - Dominating set

KW - Perfect dominating set

KW - Roman dominating function

KW - Tree

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JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

Perfect Roman domination in trees

Abstract

Keywords

ASJC Scopus subject areas

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