The Full Automorphism Groups, Determining Sets and Resolving Sets of Coprime Graphs
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DOI: 10.1007/s00373-019-02014-5
Abstract: The coprime graph is a graph $$TCG_n$$TCGn whose vertex set is $$\{1, 2, 3,\ldots ,n\}$${1,2,3,…,n}, with two vertices i and j joined by an edge if and only if $$\hbox {gcd}(i, j)= 1$$gcd(i,j)=1. In this… read more here.
Keywords: sets coprime; graph; full automorphism; resolving sets ... See more keywords
Power graphs and exchange property for resolving sets
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DOI: 10.1515/math-2019-0093
Abstract: Abstract Classical applications of resolving sets and metric dimension can be observed in robot navigation, networking and pharmacy. In the present article, a formula for computing the metric dimension of a simple graph wihtout singleton… read more here.
Keywords: power graphs; exchange property; exchange; resolving sets ... See more keywords
Edge Version of Metric Dimension and Doubly Resolving Sets of the Necklace Graph
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DOI: 10.3390/math6110243
Abstract: Consider an undirected and connected graph G = ( V G , E G ) , where V G and E G represent the set of vertices and the set of edges respectively. The concept… read more here.
Keywords: version metric; doubly resolving; dimension doubly; resolving sets ... See more keywords