*Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli, Tamil Nadu, India, E-mail: prof.jpaulraj@gmail.com
**Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli, Tamil Nadu, India, nshunmugapriya2013@gmail.com
AMS Subject Classification: Primary 05C12, Secondary 05C35.
Let G = (V, E) be a simple connected graph. An ordered subset W of V is said to be a resolving set of G if every vertex is uniquely determined by its vector of distances to the vertices in W. The minimum cardinality of a resolving set is called the resolving number of G and is denoted by r(G). In this paper, we introduce the edge cycle graph G(Ck) of a graph G and find the exact value of the resolving number for some edge cycle graphs. We also find lower and upper bounds and characterize the extremal graphs.
Resolving number, edge cycle graph
