A note on Roman k-tuple domination number

Document Type : Short notes

Authors

1 Universiti Sains Malaysia

2 Shahed University

Abstract

‎‎For an integer k2‎, ‎a Roman k-tuple dominating function‎, ‎(or just RkDF)‎, ‎in a graph G is a function f:V(G){0,1,2} satisfying the condition that every vertex u for which f(u)=0 is adjacent to at least k vertices v for which f(v)=2‎, ‎and every vertex u for which f(u)0 is adjacent to at least k1 vertices v for which f(v)=2‎. ‎The Roman k-tuple domination number of ‎G‎‎ ‎is the minimum weight of an RkDF in G. ‎In this note we settle two problems posed in [Roman k-tuple Domination in Graphs‎, ‎Iranian J‎. ‎Math‎. ‎Sci‎. ‎Inform‎. ‎15 (2020)‎, ‎101--115]‎.

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