In this study, we introduced a variant of geodetic sets which are generated by pairs of vertices and established some of its properties. For classes of path graphs, we have shown that the edge geodetic closure polynomial can be expressed in terms of a polynomial and its derivative.

geodetic set, geodetic closure polynomial.

Received: March 24, 2025; Revised: May 22, 2025; Accepted: May 26, 2025

How to cite this article: Zuraida J. Bara, Rosalio G. Artes Jr. and Regimar A. Rasid, Polynomial representation of edge geodetic closures in graphs, Advances and Applications in Discrete Mathematics 42(5) (2025), 509-514. https://doi.org/10.17654/0974165825034

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