A New Algorithm for Computing the Distance and the Diameter in Circulant Graphs

Loudiki, Laila; Kchikech, Mustapha

doi:10.3390/a18050261

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A New Algorithm for Computing the Distance and the Diameter in Circulant Graphs

by

Laila Loudiki

^*

and

Mustapha Kchikech

Polydisciplinary Faculty of Safi, Cadi Ayyad University, B.P. 4162, Safi 46000, Morocco

^*

Author to whom correspondence should be addressed.

Algorithms 2025, 18(5), 261; https://doi.org/10.3390/a18050261

Submission received: 28 March 2025 / Revised: 26 April 2025 / Accepted: 28 April 2025 / Published: 1 May 2025

(This article belongs to the Special Issue Graph Theory and Algorithmic Applications: Theoretical Developments)

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Abstract

In the present study, we focus on circulant graphs,

C_{n} (S)

, with set of vertices

{0, 1, \dots, n - 1}

and in which two distinct vertices i and j are adjacent if and only if

{| i - j |}_{n} \in S

, where S is a generating set. Despite their regularity, there are currently no established formulas to accurately determine the distance and the diameter of circulant graphs. In light of this context, we present in this paper a novel approach, which relies on a simple algorithm, capable of yielding formulas for the distance and the diameter of circulant graphs without implementing any graph.

Keywords: circulant graphs; distance; diameter

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MDPI and ACS Style

Loudiki, L.; Kchikech, M. A New Algorithm for Computing the Distance and the Diameter in Circulant Graphs. Algorithms 2025, 18, 261. https://doi.org/10.3390/a18050261

AMA Style

Loudiki L, Kchikech M. A New Algorithm for Computing the Distance and the Diameter in Circulant Graphs. Algorithms. 2025; 18(5):261. https://doi.org/10.3390/a18050261

Chicago/Turabian Style

Loudiki, Laila, and Mustapha Kchikech. 2025. "A New Algorithm for Computing the Distance and the Diameter in Circulant Graphs" Algorithms 18, no. 5: 261. https://doi.org/10.3390/a18050261

APA Style

Loudiki, L., & Kchikech, M. (2025). A New Algorithm for Computing the Distance and the Diameter in Circulant Graphs. Algorithms, 18(5), 261. https://doi.org/10.3390/a18050261

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A New Algorithm for Computing the Distance and the Diameter in Circulant Graphs

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