| Abstrakt: |
All graphs in this paper are a simple, nontrivial and connected graph G. A set W = {w1, w2,w3,..., wk} of vertex set of G, r(v\W) = (d(v,w1),d(v,w2), --, d(v,wk)) is a representation of vertex v to W, the distance between the vertex v and the vertex w, denoted by d(v,w). A set W is called a resolving set of G if every vertices of G have different representation. The minimum cardinality of resolving set W is metric dimension, denoted by dim(G). Furthermore, the resolving set W of G, is called the non-isolated resolving set if there does not for all v ∊ W induced by the non-isolated vertex. A non-isolated resolving number, denoted by nr(G), is minimum cardinality of non-isolated resolving set in G. In this research, we obtain the lower bound of the non isolated resolving number of graphs with homogeneous pendant edges, nr(G ⊙ mK1) ≤ |V(G)|m for m ≤ 2 and these results of the non isolated resolving number of graphs with homogeneous pendant edges with G with a path Pn, complete graph Kn and cycle Cn. [ABSTRACT FROM AUTHOR] |
