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Connected Resolving Partitions in Unicyclic Graphs |
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PP: 7-11 |
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Author(s) |
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Imran Javaid,
Muhammad Salman,
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Abstract |
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| A k-partition P = {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 inP 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 partitionP 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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