2024
DOI: 10.32388/ma4aus.2
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The Vertex-Edge Locating Roman Domination of Some Graphs

Abolape Deborah Akwu,
Comfort Agbaji

Abstract: In this paper, we introduce the concept of vertex-edge locating Roman dominating functions in graphs. A vertex-edge locating Roman dominating (\({ve} - {LRD}\)) function of a graph \(G = {(V,E)}\) is a function \(f:{{V{(G)}}\rightarrow{\{ 0,1,2\}}}\) such that the following conditions are satisfied: (i) for every adjacent vertices \(u,v\) with \({f{(u)}} = 0\) or \({f{(v)}} = 0\), there exists a vertex \(w\) at distance \(1\) or \(2\) from \(u\) or \(v\) with \({f{(w)}} = 2\), (ii) for every edge \({uv} \in E\… Show more

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