On 2-Resolving Sets in the Join and Corona of Graphs

Authors

DOI:

https://doi.org/10.29020/nybg.ejpam.v14i3.3977

Keywords:

resolving set, 2-resolving set, 2-metric dimension, 2-metric bases

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 ∈ 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 determine the
exact values of the 2-metric dimension of these graphs.

Author Biography

Jean Mansanadez Cabaro, Mindanao State University-Marawi

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How to Cite

Cabaro, J. M., & Rara, H. (2021). On 2-Resolving Sets in the Join and Corona of Graphs. European Journal of Pure and Applied Mathematics, 14(3), 773–782. https://doi.org/10.29020/nybg.ejpam.v14i3.3977

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