Abstract
An independent set or stable set is a set of vertices in a graph in which no two of vertices are adjacent. A set D of vertices of graph G is called a dominating set if every vertex u ϵ V(G) — D is adjacent to some vertex v ϵ D. A set S of vertices in a graph G is an independent dominating set of G if D is an independent set and every vertex not in D is adjacent to a vertex in D. By locating independent dominating set of graph G, we mean that an independent dominating set D of G with the additional properties that for u,v ϵ (V — D) satisfies N(u) ∩ D ≠ N (v) ∩ D. A minimum locating independent dominating set is a locating independent dominating set of smallest possible size for a given graph G. This size is called the locating independent dominating number of G and denoted γLi(G). In this paper, we analyze the locating independent domination number of graph operations.
Highlights
On locating independent domination number of amalgamation graphsTo cite this article: Dwi Agustin Retno Wardani et al 2017 J
Let G be a nontrivial, finite, simple, undirected and connected graphs, with vertex set V (G), edge set E(G) and with no isolated vertex, for more detail definition of graph see [1, 2]A set D of vertices of a graph G = (V, E) is dominating if every vertex in V (G) − D is adjacent to some vertex in D
A locating-dominating set of order γL(G) is called an γL(G)-set The concept of a locating dominating set was introduced and first studied by Slater [3, 4, 5, 6] and Waspodo et al [8] studied the bound of distance domination number of edge comb product
Summary
To cite this article: Dwi Agustin Retno Wardani et al 2017 J. Ser. 943 012027 View the article online for updates and enhancements. This content was downloaded from IP address 103.241.205.66 on 23/02/2018 at 04:57. Dwi Agustin Retno Wardani 1,4, Dafik, Ika Hesti Agustin, Elsa Yuli Kurniawati 1,3
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