ON THE TOTAL C3-IRREGULARITY STRENGTH OF SOME CLASSES OF GRAPHS

• Main Author: Septiadi, Irwan
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/46441
• Institution: Institut Teknologi Bandung

Let G = (V,E) be a graph admitting an H-covering. A labeling l that sends all elements of V(G) [ E(G) to a set of natural number less than or equal to k, l : V(G) [ E(G) ! f1, 2, 3, ..., kg, is called a total k-labeling. The weight of H0 that isomorphic to H is defined as wtl (H0) = åv2V(H0) l(v)+åe2E(H0) l(e). A labeling l is called an H-irregular total k-labeling of G if for any two distinct subgraphs isomorphic to H, their weight are different. The total H-irregularity strength of G, denoted by tHs(G), is the smallest positive integer k such that G has an H-irregular total k-labeling. In this project, we provide the best lower and upper bounds for the total H-irregularity strength of any graphs. We use the new lower bound to correct some mistakes that are found in Agustin dkk. (2017) and Ashraf dkk. (2019). The new lower bound is equal to the total C3-irregularity strength for some graphs, namely triangular ladders, diagonal ladders, double triangular snakes, and join of the complement of a complete graph with a path, a star, or a cycle. In the join graphs, there is some graphs that the total C3-irregularity strength is equal to the new upper bound. We also show a graph that its total H-irregularity strength is between the new lower bound and the new upper bound.