Non-inclusive and inclusive distance irregularity strength for the join product of graphs
Faisal Susanto, Kristiana Wijaya, I Wayan Sudarsana, Slamin Slamin · Electronic Journal of Graph Theory and Applications · 2022
A function ϕ : V ( G )→{1, 2, …, k } of a simple graph G is said to be a non-inclusive distance vertex irregular k -labeling of G if the sums of labels of vertices in the open neighborhood of every vertex are distinct and is said to be an inclusive distance vertex irregular k -labeling of G if the sums of labels of vertices in the closed neighborhood of each vertex are different. The minimum k for which G has a non-inclusive (resp. an inclusive) distance vertex irregular k -labeling is called a non-inclusive (resp. an inclusive) distance irregularity strength and is denoted by d i s ( G ) (resp. by d i s ( G ) ). In this paper, the non-inclusive and inclusive distance irregularity strength for the join product graphs are investigated.