Open AccessOn the resolving strong domination number of some wheel related graphs
Author(s) -
R Humaizah,
Dafik Dafik,
Arika Indah Kristiana,
Ika Hesti Agustin,
Elsa Yuli Kurniawati
Publication year - 2022
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 - 10.1088/1742-6596/2157/1/012015
Subject(s) - domination analysis , dominating set , mathematics , combinatorics , graph , notation , cardinality (data modeling) , set (abstract data type) , discrete mathematics , dimension (graph theory) , computer science , vertex (graph theory) , arithmetic , data mining , programming language
This study aims to analyse the resolving strong dominating set. This concept combinations of two notions, they are metric dimension and strong domination set. By a resolving strong domination set, we mean a set D s ⊂ V ( G ) which satisfies the definition of strong dominating set as well as resolving set. The resolving strong domination number of graph G , denoted by γ rst ( G ), is the minimum cardinality of resolving strong dominating set of G . In this paper, we determine the resolving strong domination number of some wheel related graphs, namely helm graph H n , gear graph G n , and flower graph Fl n . Through this paper, we will use the notations γ st ( G ) and dim ( G ) which show the strong domination and dimension numbers.