Restrained double Roman domination of a graph release_bhrlqt4lzffmbdlr7tpjebwfeu

by Doost Ali Mojdeh, Iman Masoumi, Lutz Volkmann

Released as a article .

2021  

Abstract

For a graph G=(V,E), a restrained double Roman dominating function is a function f:V→{0,1,2,3} having the property that if f(v)=0, then the vertex v must have at least two neighbors assigned 2 under f or one neighbor w with f(w)=3, and if f(v)=1, then the vertex v must have at least one neighbor w with f(w)≥2, and at the same time, the subgraph G[V_0] which includes vertices with zero labels has no isolated vertex. The weight of a restrained double Roman dominating function f is the sum f(V)=∑_v∈Vf(v), and the minimum weight of a restrained double Roman dominating function on G is the restrained double Roman domination number of G. We initiate the study of restrained double Roman domination with proving that the problem of computing this parameter is NP-hard. Then we present an upper bound on the restrained double Roman domination number of a connected graph G in terms of the order of G and characterize the graphs attaining this bound. We study the restrained double Roman domination versus the restrained Roman domination. Finally, we characterized all trees T attaining the exhibited bound.
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Date   2021-06-16
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arXiv  2106.08501v1
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