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2-Size Resolvability in Graphs |
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PP: 371-376 |
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Author(s) |
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M. Salman,,
I. Javaid,
M. A. Chaudhry,
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Abstract |
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| 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.
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