Abstract
The local resolving neighborhood of a pair of vertices for and is if there is a vertex in a connected graph where the distance from to is not equal to the distance from to , or defined by . A local resolving function of is a real valued function such that for and . The local fractional metric dimension of graph denoted by , defined by In this research, the author discusses about the local fractional metric dimension of comb product are two graphs, namely graph and graph , where graph is a connected graphs and graph is a complate graph and denoted by We get
Highlights
The first authers to discuss the minimum0resolving set and the metric0dimension problems is [1, 2]. They assumed that the graph used is a connected graph, simple graph and a finite graph
In this research, we investigate the fractional local metric0dimension of comb product graphs where H are some special graphs
1 n is a local resolving function of G and |g| = 1. It follows from the definition of local resolving function that 1 ≤ dimfl(G) ≤ dimf(G) for any connected graph G, that dimfl(Cn) = 1
Summary
The first authers to discuss the minimum0resolving set and the metric0dimension problems is [1, 2]. Abstract: For the connected graph G with vertex set V(G) and edge set E(G), the local resolving neighborhood The fractional local metric0dimension of graph G denoted dimfl(G), is defined by dimfl(G) = min{|fl|: flisalocalresolvingfunctionofG}. In [5, 6] studied the commutative0characterization0of graph operations with0respect to the local metric0dimension and metric dimension, respectively.
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