# On the local fractional metric dimension of corona product graphs

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## Abstract

A vertex in a connected graph is said to resolve a pair of vertices {u, v} in if the distance from to is not equal to the distance from v to x. A set of vertices of is a resolving set for G if every pair of vertices is resolved by some vertices of S. The smallest cardinality of a resolving set for G is called the metric dimension of G, denoted by dim(G). For the pair of two adjacent vertices {u, v} is called the local resolving neighbourhood and denoted by R 1{u, v}. A real valued function g 1: V(G) → [0,1] is a local resolving function of G if for every two adjacent vertices u, v ∈ V(G). The local fractional metric dimension of G is defined as dimft(G) = min{|g 1|: g 1 is local resolving function of G} where |g 1| = ∑v∈V g 1(v). Let and be two graphs of order n 1 and n 2, respectively. The corona product Go H is defined as the graph obtained from G and H by taking one copy of G and n 1 copies of H and joining by an edge each vertex from the ith -copy of H with the ith -vertex of G. In this paper we study the problem of finding exact values for the fractional local metric dimension of corona product of graphs.

Original language English 012043 IOP Conference Series: Earth and Environmental Science 243 1 https://doi.org/10.1088/1755-1315/243/1/012043 Published - 9 Apr 2019 1st International Conference on Environmental Geography and Geography Education, ICEGE 2018 - Jember, East Java, IndonesiaDuration: 17 Nov 2018 → 18 Nov 2018

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