Journal
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;//doi.org/10.29020/nybg.ejpam.v14i3.3977 |
URL | http://www.ejpam.com |