2-Size Resolvability in Graphs

Authors

M. Salman,, Centre for advanced studies in Pure and Applied Mathematics, Bahauddin Zakariya University Multan 60800, PakistanFollow
I. Javaid
M. A. Chaudhry

Author Country (or Countries)

Pakistan

Abstract

A vertex u in a graph G resolves a pair of distinct vertices x, y of G if the distance between u and x is different from the distance between u and y. A set W of vertices in G resolves the graph G if every pair of distinct vertices of G is resolved by some vertices in W. The metric dimension of a graph, denoted by dim(G), is the smallest cardinality of a resolving set. A resolving set W for a connected graph G of order n ¸ 3 is called 2-size resolving set if the size of the subgraph < W > induced by W is two. The minimum cardinality of a 2-size resolving set is called the 2-size metric dimension of G, denoted by tr(G). A 2-size resolving set of cardinality tr(G) is called a tr-set. In this paper, we study 2-size resolving sets in some well-known classes of graphs and give some realizable results.

Suggested Reviewers

N/A

Recommended Citation

Salman,, M.; Javaid, I.; and A. Chaudhry, M. (2012) "2-Size Resolvability in Graphs," Applied Mathematics & Information Sciences: Vol. 06: Iss. 2, Article 26.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol06/iss2/26