Connected Resolving Partitions in Unicyclic Graphs
نویسندگان
چکیده
A k-partition Π = {S1,S2, . . . ,Sk} of V (G) is resolving if for every two distinct vertices u and v of a connected graph G, there is a set Si in Π so that the minimum distance between u and a vertex of Si is different from the minimum distance between v and a vertex of Si. A resolving partition Π is said to be connected if each subgraph < Si > induced by Si (1 ≤ i ≤ k) is connected in G. In this paper, we investigate the minimum connected resolving partitions in unicyclic graphs. Also, modified sharp lower and upper bounds for the connected partition dimension of unicyclic graphs are provided.
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