# On The Metric Dimension with Non-isolated Resolving Number of Some Exponential Graph

• S. M. Yunika CGANT University of Jember; Mathematics Depart. University of Jember
• Slamin Slamin CGANT University of Jember; System Information. Depart. University of Jemb
• Dafik Dafik CGANT University of Jember; Mathematics Edu. Depart. University of Jember
• Kusbudiono Kusbudiono CGANT University of Jember; Mathematics Depart. University of Jember

### Abstract

Let w, w ∈ G = (V, E). A distance in a simple, undirected and connected graph G, denoted by d(v, w), is the length of the shortest path between v and w in G. For an ordered set W = {w1, w2, w3, . . . , wk} of vertices and a vertex v ∈ G, the ordered k-vector r(v|W) = (d(v, w1), d(v, w2), . . . , d(v, wk)) is representations of v with respect to W. The set W is called a resolving set for G if distinct vertices of G have distinct representations with respect to W. The metric dimension dim(G) of G is the minimum cardinality of resolving set for G. The resolving set W of graph G is called non-isolated resolving set if subgraph W is induced by non-isolated vertex. While the minimum cardinality of non-isolated resolving set in graph is called a non-isolated resolving number, denoted by nr(G). In this paper we study a metric dimension with non-isolated resolving number of some exponential graph.
Published
2017-08-08
How to Cite
YUNIKA, S. M. et al. On The Metric Dimension with Non-isolated Resolving Number of Some Exponential Graph. UNEJ e-Proceeding, [S.l.], p. 328-330, aug. 2017. Available at: <https://jurnal.unej.ac.id/index.php/prosiding/article/view/4257>. Date accessed: 14 aug. 2024.
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General