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

##### Date

2017-08-08##### Author

YUNIKA, S.M.

SLAMIN, Slamin

DAFIK, Dafik

KUSBUDIONO, Kusbudiono

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Show full item record##### 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

##### Collections

- LSP-Conference Proceeding [1872]

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