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| The Local Fractional Metric Dimension of Corona Product of Complete Graph and Cycle Graph |
Siti Aisyah, Ratna Dwi C., Mohammad Imam Utoyo and Liliek Susilowati
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Abstract:
A vertex in a connected graph is said to resolve a pair of vertices in if the distance from to is not equal to the distance from to . A set of vertices of is a resolving set for if every pair of vertices is resolved by some vertices of . The smallest cardinality of a resolving set for is called the metric dimension of , denoted by . For the pair of two adjacent vertices is called the local resolving neighbourhood and denoted by . A real valued function is a local resolving function of if for every two adjacent vertices . The local fractional metric dimension of is defined as
where Let and be two graphs of order and , respectively. The corona product is defined as the graph obtained from and by taking one copy of and copies of and joining by an edge each vertex from the -copy of with the -vertex of . In this paper we study the problem of finding exact values for the fractional local metric dimension of corona product of graphs.
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