Open AccessOn resolving domination number of friendship graph and its operation
Author(s) -
S. Kurniawati,
. Slamin,
Dafik Dafik,
Dwi Agustin Retno Wardani,
Ermita Rizki Albirri
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1465/1/012019
Subject(s) - dominating set , combinatorics , mathematics , vertex (graph theory) , domination analysis , graph , connectivity , discrete mathematics , cardinality (data modeling) , computer science , data mining
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 , …, w k } 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, w k )), 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 γ r ( G ). In this paper, we discussed the resolving domination number of friendship graphs and its operation.