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Title On 2-Resolving Sets in the Join and Corona of Graphs
Posted by Helen Rara
Authors Jean Cabaro and Helen M. Rara
Publication date July, 2021
Journal European Journal of Pure and Applied Mathematics
Volume 14
Issue No. 3, 2021
Pages 773 - 782
Publisher New York Business Global
Abstract Let G be a connected graph. An ordered set of vertices {v1, ...,vl} is a 2-resolving set in G if, for any distinct vertices u, w in V (G), the lists of distances (dG(u, v1),..., dG(u; vl)) and (dG(w, v1),..., dG(w; vl)) differ in at least 2 positions. If G has a 2-resolving set, we denote the least size of a 2-resolving set by dim2(G), the 2-metric dimension of G. A 2-resolving set of size dim2(G) is called a 2-metric basis for G. This study deals with the concept of 2-resolving set of a graph. It characterizes the 2-resolving set in the join and corona of graphs and determines the exact values of the 2-metric dimension of these graphs.
Index terms / Keywords resolving set, 2-resolving set, 2-metric dimension, 2-metric basis, join, corona
DOI https;//