11,533 research outputs found
On Classes of Neighborhood Resolving Sets of a Graph
Let G=(V,E) be a simple connected graph. A subset S of V is called a neighbourhood set of G if G=\bigcup_{s\in S}<N[s]>, where N[v] denotes the closed neighbourhood of the vertex v in G. Further for each ordered subset S={s_1,s_2, ...,s_k} of V and a vertex , we associate a vector with respect to S, where d(u,v) denote the distance between u and v in G. A subset S is said to be resolving set of G if for all . A neighbouring set of G which is also a resolving set for G is called a neighbourhood resolving set (nr-set). The purpose of this paper is to introduce various types of nr-sets and compute minimum cardinality of each set, in possible cases, particulary for paths and cycles
On the limiting distribution of the metric dimension for random forests
The metric dimension of a graph G is the minimum size of a subset S of
vertices of G such that all other vertices are uniquely determined by their
distances to the vertices in S. In this paper we investigate the metric
dimension for two different models of random forests, in each case obtaining
normal limit distributions for this parameter.Comment: 22 pages, 5 figure
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