On inclusive d-distance irregularity strength on triangular ladder graph and path
Budi Utami, Kiki Ariyanti Sugeng, Suarsih Utama · AKCE International Journal of Graphs and Combinatorics · 2020
The length of a shortest path between two vertices u and v in a simple and connected graph G, denoted by d(u, v), is called the distance of u and v. An inclusive vertex irregular d-distance labeling is a labeling defined as such that the vertex weight, that is are all distinct. The minimal value of the largest label used over all such labeling of graph G, denoted by is defined as inclusive d-distance irregularity strength of G. Others studies have concluded the lower bound value of and the value of In this paper, we generalize the lower bound value of for We used the lower bound value of and the previous result of to investigate the value of As a result, we found the exact values of for the cases n = 7, and the value of the upper bound of for other n. We also found the relation of the value of and the value of Further investigation on path brought us to conclude the exact value of and for some n.