The local metric dimension of split and unicyclic graphs

The local metric dimension of split and unicyclic graphs

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A set W is called a local resolving set of G if the distance of u and v to some elements of W are distinct for every two adjacent Cotton Tipped Cleaning Sticks vertices u and v in G.The local metric dimension of G is the minimum cardinality of a local resolving set of G.A connected graph G is called a split graph if V(G) can be partitioned into two subsets V1 and V2 where an induced subgraph of G by V1 and V2 is a complete graph and an independent set, respectively.We also consider a graph, namely the unicyclic graph which is a connected 162mm Diameter graph containing exactly one cycle.In this paper, we provide a general sharp bounds of local metric dimension of split graph.

We also determine an exact value of local metric dimension of any unicyclic graphs.