An Inclusive Distance Irregularity Strength of n-ary Tree

Kristiana Wijaya; Safira Nur Aulia; Ikhsanul Halikin; Kusbudiono Kusbudiono

doi:10.31764/jtam.v8i2.20549

An Inclusive Distance Irregularity Strength of n-ary Tree

Kristiana Wijaya, Safira Nur Aulia, Ikhsanul Halikin, Kusbudiono Kusbudiono

Abstract

An inclusive distance vertex irregular labelling of a simple graph G is a function of the vertex set of to positive integer set such that the sum of its vertex label and the labels of all vertices adjacent to the vertex are distinct. The minimum of maximum label of the vertices is said to be inclusive distance irregularity strength of G, denoted by dis(G). The purpose of this research is showing that dis(T_{n,2})= (n^2+2)/2 where T_{n,2} is a complete n-ary tree to level two.

Keywords

Irregular labelling; Inclusive; Vertex weight; Complete n-ary tree

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DOI: https://doi.org/10.31764/jtam.v8i2.20549