Title

Perfect Roman domination in trees

Document Type

Article

Publication Date

2-19-2018

Subject Area

ARRAY(0x55597f97d2f8)

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.

Publication Title

Discrete Applied Mathematics

Volume

236

First Page

235

Last Page

245

Digital Object Identifier (DOI)

10.1016/j.dam.2017.10.027

ISSN

0166218X

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