Discrete Applied Mathematics
Resolvability in graphs and the metric dimension of a graph
Discrete Applied Mathematics
Locating and total dominating sets in trees
Discrete Applied Mathematics
| Hi-index | 0.04 |
Given an ordered partition @P={P"1,P"2,...,P"t} of the vertex set V of a connected graph G=(V,E), the partition representation of a vertex v@?V with respect to the partition @P is the vector r(v|@P)=(d(v,P"1),d(v,P"2),...,d(v,P"t)), where d(v,P"i) represents the distance between the vertex v and the set P"i. A partition @P of V is a resolving partition of G if different vertices of G have different partition representations, i.e., for every pair of vertices u,v@?V, r(u|@P)r(v|@P). The partition dimension of G is the minimum number of sets in any resolving partition of G. In this paper we obtain several tight bounds on the partition dimension of trees.