The resolving graph of amalgamation of cycles - Iswadi H.; Baskoro E.T.; Salman A.N.M.; Simanjuntak R. (Utilitas Mathematica, 2010)
For an ordered set W = w1, w2,⋯, w k of vertices and a vertex v in a connected graph G, the representation of v with respect to W is the ordered k-tuple r(v|W) = (d(v,w1),d(v,w2),⋯ ,d(v,wk)) where d(x, y) represents the distance between the vertices x and y. The set W is called a resolving set for G if every vertex of G has a distinct representation. A resolving set containing a minimum number of vertices is called a basis for G. The dimension of G, denoted by dim(G), is the number of vertices in a basis of G. A resolving set W of G is connected if the subgraph (W) induced by W is a nontrivial connected subgraph of G. The connected resolving number is the minimum cardinality of a connected resolving set in a graph G, denoted by cr(G). A cr-set of G is a connected resolving set with cardinality cr(G). A connected graph H is a resolving graph if there is a graph G with a cr-set W such that (W) = H. Let Gi be a finite collection of graphs and each G i has a fixed vertex voi called a terminal. The amalgamation AmalGi, voi is formed by taking of all the Gi's and identifying their terminals. In this paper, we determine the connected resolving number and characterize the resolving graphs of amalgamation of cycles.