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Exploring the Total Distance Vertex Irregular Labeling of Some Wheel-Related Graphs and Its Computation

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  • M. Basher

Abstract

Consider a simple graph ζ characterized by a vertex set Vζ and an edge set Eζ. A distance vertex irregular total m-labeling (DVITL) is a total m-labeling from the set of vertices and edges, Vζ∪Eζ, into a set of positive integers 1,2,…,m, where the vertex weights of any couple of separate vertices are different. The weight of a vertex x∈Vζ is the sum of the labels of all vertices adjacent to x and the labels of all edges incident to x. The total distance vertex irregularity strength of graph ζ, denoted as tdis ζ, is described as the lowest value of m for which there exists a total distance vertex irregular labeling of ζ. The paper presents a calculation of the precise total distance vertex irregularity strength for several families of wheel graphs. These families are obtained through the subdivision of the wheel graphs into spokes, cycles, and barycentric subdivisions. We present the Python code implementation intended for executing DVITL on such graphs.

Suggested Citation

  • M. Basher, 2026. "Exploring the Total Distance Vertex Irregular Labeling of Some Wheel-Related Graphs and Its Computation," Journal of Mathematics, Hindawi, vol. 2026, pages 1-30, August.
    • Handle: RePEc:hin:jjmath:3012344
    DOI: 10.1155/jom/3012344
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