Upper Bounds on Inclusive Distance Vertex Irregularity Strength.

An inclusive distance vertex irregular labeling of a graph G is an assignment of positive integers { 1 , 2 , ... , k } to the vertices of G such that for every vertex the sum of numbers assigned to its closed neighborhood is different. The minimum number k for which exists an inclusive distance vertex irregular labeling of G is denoted by dis ^ (G) . In this paper we prove that for a simple graph G on n vertices in which no two vertices have the same closed neighborhood dis ^ (G) ≤ n 2 . [ABSTRACT FROM AUTHOR]