Total resolving number of edge cycle graphs

Abstract

Let 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 Total resolving number is the minimum cardinality taken over all resolving sets in which has no isolates and it is denoted by In this paper, we determine the exact values of total resolving number of and Also, we obtain bounds for the total resolving number of when G is an arbitrary graph and characterize the extremal graphs.

Keywords

• resolving number
• total resolving number
• edge cycle graph