On Distance Vertex Irregular Total k-Labeling

Dian Eka Wijayanti, Noor Hidayat, Diari Indriati, Abdul Rouf Alghofari, Slamin

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:TS→1,2,· · · ,k, be a total k-labeling on H and wσ(x), be a weight of xT 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 xT 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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Authors

Dian Eka Wijayanti
dian@math.uad.ac.id (Primary Contact)
Noor Hidayat
Diari Indriati
Abdul Rouf Alghofari
Slamin
Wijayanti, D. E., Hidayat, N., Indriati, D. ., Alghofari, A. R. ., & Slamin. (2023). On Distance Vertex Irregular Total k-Labeling. Science and Technology Indonesia, 8(3), 479–485. https://doi.org/10.26554/sti.2023.8.3.479-485

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