Computing the precise total distance vertex irregularity strength of prism and web graphs

Articles in Press

Document Type : Original paper

Authors

1 Department of Mathematics, College of Science, Qassim University, P. O. Box 6644, Buraydah,51452, Saudi Arabia

2 Department of Mathematics and Computer Science, Faculty of Science, Suez University, P.O.Box:43221, Suez, Egypt

3 Department of Applied Mathematics and Informatics, Technical University, Letn´a 9, Koˇsice, Slovakia

Abstract

Given a graph $\Gamma\left(V, E\right)$ with a non-empty vertex set $V$ and edge set $E$. A total $d$-labeling is the allocation of positive integers to the collection $V(\Gamma) \cup E(\Gamma)$. A labeling is termed distance vertex irregular total d-labeling (DVITL) if any two distinct vertices in $V$ possess different weights. The weight of the vertex $u \in V$ is the aggregate of labels of the neighbor vertices and the labels of edges that incident at the vertex $u$. The least number $d$ for which there exists a DVITL of $\Gamma$ is referred to as the total distance vertex irregularity strength of $\Gamma$ symbolized by $\operatorname{tdis}(\Gamma)$. In this research, we compute the precise values of the total distance vertex irregularity strength for prism graphs, web graphs, and web graphs without center.

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References

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Communications in Combinatorics and Optimization

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Available Online from 01 May 2026

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