On resolving domination number of friendship graph and its operation. (February 2020)

• Record Type: Journal Article
• Authors: Kurniawati, S; Slamin, ; Dafik, ; Wardani, D A R; Albirri, E R
• Is Part Of: Journal of physics. Volume 1465(2020)
• Publication Date: 2020-02
• Subjects: Physics -- Congresses; 530.5
• DOI: 10.1088/1742-6596/1465/1/012019
• Languages: English
• ISSNs: 1742-6588

Abstract

Abstract: Let G = ( V, E ) be a simple, finite, and connected graph of order n . A dominating set D ⊆ V ( G ) such every vertex not in D is adjacent to at least one member of D . A dominating set of smallest size is called a minimum dominating set and it is known as the domination number. The domination number is the minimum cardinality of a dominating set and denoted by γ ( G ). The other hand, for an ordered set W = { w 1, w 2, w 3, …, wk } of vertices and a vertex v in a connected graph G, the (metric) representation of v with respect to W is the k − vector r ( v | W ) = ( d ( v, w 1 ), d ( v, w 2 ), d ( v, w 3 ), …, d ( v, wk )), where d ( x, y ) represents the distance between the vertices x and y . The set W is a resolving set for G if distinct vertices of G have distinct representations with respect to W . A resolving set of minimum cardinality is called a minimum resolving set or a basis and the cardinality of a basis for G is its metric dimension dim ( G ). A Set of vertices of a graph G that is both resolving and dominating is a resolving dominating set. The minimum cardinality of a resolving dominating set is called resolving domination number γr ( G ). In this paper, we discussed the resolving domination number of friendship graphs and its operation.