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Diari Indriati
Department of Mathematics, Universitas Sebelas Maret, Surakarta, 57126, Indonesia
Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Environmental Science Materials Science & Nanotechnology Physics

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On Distance Vertex Irregular Total k-Labeling Dian Eka Wijayanti; Noor Hidayat; Diari Indriati; Abdul Rouf Alghofari; Slamin
Science and Technology Indonesia Vol. 8 No. 3 (2023): July
Publisher : Research Center of Inorganic Materials and Coordination Complexes, FMIPA Universitas Sriwijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26554/sti.2023.8.3.479-485

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).
Co-Authors Abdul Rouf Alghofari Hidayat, Noor Slamin Wijayanti, Dian Eka