• TOTAL RESOLVING NUMBER OF EDGE CYCLE GRAPHS G(C3)

Abstract

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).  Total resolving number as the minimum cardinality taken over all resolving sets in which   has no isolates and is denoted by tr(G). In this paper, we determine the exact values for the total resolving number of T(C₃), C_n(C₃) and F_s(C₃). Also, we obtain bounds for the total resolving number of G(C₃) and characterize the extremal graphs.