ENTIRE IRREGULARITY STRENGTH OF TRIANGULAR BOOK GRAPHS - Muhammad Issaac, Gardhani
The total vertex irregularity strength and the total edge irregularity strength were first introduced by Baca et al at [1]. Marzuki et al [6] then combined both concept above by introducing the total irregularity strength. On the other hand, Muthugurupackiam [9] introduced the total face irregularity strength. Motivated by all papers above, we introduced entirely irregular total k-labeling and entire irregularity strength. Let G = (V;E; F) is a 2-connected plane graph with set of vertices V , set of edges E, and set of faces F. A total labeling : V [ E ! f1; 2; :::; kg is called entirely irregular total k-labeling if for any two different vertices, for two any different edges, and for any two different faces, they have different weight. The weight of a vertex is defined as sum of the vertex’s label and every label of edges that adjancent to the vertex. The weight of an edge is sum of the edge’s label and labels of two vertices which is its endpoints. The weight of a face is sum of every label of vertices and edges on the boundary of the face. The minimum k for which G has entirely irregular total k-labeling is called entire irregularity strength, denoted by ets(G). In this paper, we give a lower bound and upper bound of ets(G). Furthermore, we determine ets(G) for a triangular books graph G.