Science and Technology Indonesia
Vol. 8 No. 3 (2023): July

On Distance Vertex Irregular Total k-Labeling

Dian Eka Wijayanti (Department of Mathematics, Universitas Ahmad Dahlan, Kampus IV UAD, Yogyakarta, 55166, Indonesia)
Noor Hidayat (Department of Mathematics, Universitas Brawijaya, Malang, 65145, Indonesia)
Diari Indriati (Department of Mathematics, Universitas Sebelas Maret, Surakarta, 57126, Indonesia)
Abdul Rouf Alghofari (Department of Mathematics, Universitas Brawijaya, Malang, 65145, Indonesia)
Slamin (Department of Informatics, University of Jember, Jember, 68121, Indonesia)

Article Info

Publish Date
06 Jul 2023

Abstract

Let H= (T,S), be a finite simple graph, T(H)= T and S(H)= S, respectively, are the sets of vertices and edges on H. Let σ:T∪S→1,2,· · · ,k, be a total k-labeling on H and wσ(x), be a weight of x∈T while using σ labeling, which is evaluated based on the total number of all vertices labels in the neighborhood x and its incident edges. If every x∈T has a different weight, then σ is a distance vertex irregular total k-labeling (DVITL). Total distance vertex irregularity strength of H (tdis(H) is defined as the least k for which H has a DVITL. Our research investigates the DVITL of the path (Pr) and cycle (Cr) graphs. We establish a lower bound and then calculate the precise value of tdis(Pr) and tdis(Cr).

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Journal Info
Science and Technology Indonesia
Website

Abbrev

JSTI

Publisher

Universitas Sriwijaya

Subject

Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Environmental Science Materials Science & Nanotechnology Physics

Description

An international Peer-review journal in the field of science and technology published by The Indonesian Science and Technology Society. Science and Technology Indonesia is a member of Crossref with DOI prefix number: 10.26554/sti. Science and Technology Indonesia publishes quarterly (January, April, ...