TOTAL RESOLVING NUMBER OF CORONA OF GRAPHS AND COMPLETE GRAPHS
Let be a simple connected graph. If is an ordered set, then the ordered k-tuple is called the representation of v with respect to W and it is denoted by W is called a resolving set for G if all the vertices of have distinct representations. The minimum cardinality of a resolving set is called the resolving number of G and it is denoted by The total resolving number as the minimum cardinality taken over all resolving sets in which has no isolates and it is denoted by The corona of two graphs G and H, is the graph formed from one copy of G and copies of H where the ith vertex of G is adjacent to every vertex in the ith copy of H. In this paper, we determine the exact values of total resolving number of Also, we determine the lower and upper bounds of total resolving number of and characterize the extremal graphs.
resolving number, total resolving number, corona of graphs.