TY - JOUR

T1 - On inclusive d-distance irregularity strength on triangular ladder graph and path

AU - Utami, Budi

AU - Sugeng, Kiki A.

AU - Utama, Suarsih

PY - 2020/1/1

Y1 - 2020/1/1

N2 - 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.

AB - 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.

KW - inclusive d-distance irregularity strength

KW - path

KW - Triangular ladder graph

UR - http://www.scopus.com/inward/record.url?scp=85084288438&partnerID=8YFLogxK

U2 - 10.1016/j.akcej.2019.10.003

DO - 10.1016/j.akcej.2019.10.003

M3 - Article

AN - SCOPUS:85084288438

JO - AKCE International Journal of Graphs and Combinatorics

JF - AKCE International Journal of Graphs and Combinatorics

SN - 0972-8600

ER -