On inclusive d-distance irregularity strength on triangular ladder graph and path

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Abstract

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 (Formula presented.) such that the vertex weight, that is (Formula presented.) are all distinct. The minimal value of the largest label used over all such labeling of graph G, denoted by (Formula presented.) is defined as inclusive d-distance irregularity strength of G. Others studies have concluded the lower bound value of (Formula presented.) and the value of (Formula presented.) In this paper, we generalize the lower bound value of (Formula presented.) for (Formula presented.) We used the lower bound value of (Formula presented.) and the previous result of (Formula presented.) to investigate the value of (Formula presented.) As a result, we found the exact values of (Formula presented.) for the cases (Formula presented.) n = 7, and the value of the upper bound of (Formula presented.) for other n. We also found the relation of the value of (Formula presented.) and the value of (Formula presented.) Further investigation on path brought us to conclude the exact value of (Formula presented.) and (Formula presented.) for some n.

Original languageEnglish
JournalAKCE International Journal of Graphs and Combinatorics
DOIs
Publication statusAccepted/In press - 1 Jan 2020

Keywords

  • inclusive d-distance irregularity strength
  • path
  • Triangular ladder graph

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