The Fractional Local MetricDimension of CombProduct Graphs

Authors

S. Aisyah, Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Kaltara, Indonesia.Follow
Mohammad Imam Utoyo, Department of Mathematics, Faculty ofScience and Technology, University of Airlangga, IndonesiaFollow
Liliek Susilowati, Department of Mathematics, Faculty ofScience and Technology, University of Airlangga, IndonesiaFollow

Abstract

For the connected graph G with vertex set V(G)and edge set E(G), the localresolvingneighborhood R1{u,v}of two adjacent vertices u,v isdefined by R1{u,v}={ x ꞓ v(G):d(x,u)≠��d(x,v)}. A local resolving0function f1of G is a real valued function f1:V(G)→[0,1]such0 that f1(R1{u,v})≥1 for every two adjacent u,v vertices u,v ꞓ (x,v).Thefractional local metric dimension of graph G denoted dim f1(G), is defined by dim f1(G)=min⁡{| f1|:f1}.One of the operation in graph is the comb product graphs. The comb product graphs of G and H is denoted by ��G ⊳ H⊳��.The purpose of this research is to determine the fractionallocal metric dimension of G ⊳ H ,forgraph ��is a connected graph and graph His a complete graph (����).The result of ��⊳����is ����������(��⊳����)=|��v (��)|.����������(����−1).

Keywords

local fractional metric dimension, resolving function, comb product graphs.

Article Type

Article

How to Cite this Article

Aisyah, S.; Utoyo, Mohammad Imam; and Susilowati, Liliek (2020) "The Fractional Local MetricDimension of CombProduct Graphs," Baghdad Science Journal: Vol. 17: Iss. 4, Article 6.
DOI: https://doi.org/10.21123/bsj.2020.17.4.1288