MODULAR IRREGULAR LABELING OF DOUBLE BROOM GRAPH

• Main Author: Elysia Chungdinata, Stephanie
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/81489
• Institution: Institut Teknologi Bandung

Let G = (V, E) be a graph of order n with nonempty vertex set V and edge set E. Let t be a positive integer. A modular irregular labeling of graph G is an edge t-labeling ? : E ? [1, t] such that there exists a bijective weight function wt? : V ? Zn, where Zn be a group of modulo n. The modular weight function of vertex u defined by wt?(u) = P v?N(u) ?(uv). Furthermore, ms(G) denote the modular irregularity strength of graph G that is the minimum number t such that a graph G has modular irregular labeling with largest label t. Let k, l be a positive integer. The double broom which denoted by DBk,l is a graph of order k + 2l which obtained by identifying each pendant vertices z1 and zk of path graph of order k with center vertex of each star graph of order l + 1. In this research, we construct the modular irregular labeling for double broom graph and determine the exact value of the modular irregularity strength for large enough k + 2l.