Non-inclusive and inclusive distance irregularity strength for the join product of graphs

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