On The Total Vertex Irregularity Strength of Comb Product of Cycle and Other Graph
Rismawati Ramdani
UIN Sunan Gunung Djati Bandung
Abstract
Let G be a graph and k be a positive integer. A total k-labeling of G is a map f from vertex set union edge set of G to integers 1,2,3, until k. The vertex weight v under the labeling f is the sum of the label of v and the label of edges incident with v. A total k labeling of G is called vertex irregular if there are no two vertices with the same weight. The total vertex irregularity strength of G is the minimum k such that G has a vertex irregular total k-labeling. Let G and H be two connected graphs. Let o be a vertex of H . The comb product between G and H in the vertex o is a graph obtained by taking one copy of G and cardinality of G copies of H and grafting the i th copy of H at the vertex o to the i th vertex of G. In this paper, we determine the total vertex irregularity strength of come product of cycle and other graph.
Keywords: Comb product graph, cycle, the total vertex irregularity strength, total vertex irregular labeling.
Topic: Mathematics