| Abstrak/Abstract |
Abstract. For any simple undirected graph G(V,E), a map f : V ?E ? {1,2,...,k} such that for any di?erent edges xy and x0y0 their weights are distinct is called an edge irregular total k-labeling. The weight of edge xy is de?ned as the sum of edge label of xy, vertex label of x and vertex label of y. The minimum k for which the graph G has an edge irregular total k-labeling is called the total edge irregularity strength of G and is denoted by tes(G). In this paper, we determine the exact value of the total edge irregularity strength of odd arithmetic book graph Bn(C3,5,7,...2n+1) and even arithmetic book graph Bn(C4,6,8,...,2n+2) of n sheets. We found that the tes of odd arithmetic book graph Bn(C3,5,7,...,2n+1) of n sheets is equal to the ceiling function of n2+n+3 3 and the tes of even arithmetic book graph Bn(C4,6,8,...,2n+2) is equal to the ceiling function of n2+2n+3 3 |
