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Computing Exact Edge Geodetic Numbers in K-Powered Path and Cycle Graphs

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  • A. Baniabedalruhman
  • Basem Alkhamaiseh
  • M. M. M. Jaradat

Abstract

For any two vertices u and v in a graph G, u−v geodesic is the shortest path between u and v. A set S of vertices in G is called an edge geodetic cover for G if every edge in G belongs to a geodesic between two vertices of S. The minimum cardinality of an edge geodetic cover is called the edge geodetic number and is denoted by egG. In this paper, we determine the exact edge geodetic number of k-powered paths and k-powered cycles. The proofs rely on a careful characterization of semiextreme vertices and geodesic covering arguments. The obtained results extend previous work on edge geodetic parameters and provide new insights into metric properties of graph powers.

Suggested Citation

  • A. Baniabedalruhman & Basem Alkhamaiseh & M. M. M. Jaradat, 2026. "Computing Exact Edge Geodetic Numbers in K-Powered Path and Cycle Graphs," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2026, pages 1-6, August.
    • Handle: RePEc:hin:jijmms:6398287
    DOI: 10.1155/ijmm/6398287
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