## 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 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 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 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.

Original language | English |
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Article number | 012043 |

Journal | IOP Conference Series: Earth and Environmental Science |

Volume | 243 |

Issue number | 1 |

DOIs | |

Publication status | Published - 9 Apr 2019 |

Event | 1st International Conference on Environmental Geography and Geography Education, ICEGE 2018 - Jember, East Java, Indonesia Duration: 17 Nov 2018 → 18 Nov 2018 |