On the local fractional metric dimension of corona product graphs
Siti Aisyah, Mohammad Imam Utoyo, Liliek Susilowati · IOP Conference Series Earth and Environmental Science · 2019
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 dim ft ( 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 G⊙ 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 i th -copy of H with the i th -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.