| Keywords and phrases: hypergroup, distance-regular graph, intersection array, diameter, structure of hypergroup associated with a distance-regular graph, Heawood graph, (4,6)-cage.
Received: October 30, 2024; Accepted: November 20, 2024; Published: December 17, 2024
How to cite this article: Masakazu Nihei, On the hypergroup associated with a distance-regular graph with the intersection array {k, k – 1, k – c; 1, c, k}, Universal Journal of Mathematics and Mathematical Sciences 21(1) (2025), 1-12. https://doi.org/10.17654/2277141725001
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License  
References
[1] N. Biggs, Algebraic Graph Theory, Cambridge University Press, 1974.
[2] C. Godsil and G. Royle, Algebraic graph theory, Graduate Texts in Mathematics, Springer, 2001.
[3] R. B. Bapat, Graphs and Matrices, Springer, 2010.
[4] R. Ichihara, S. Kawakami and M. Sakao, Hypergroup extensions of finite abelian groups by hypergroups of order two, Nihonkai Math. J. 21 (2010), 47-71.
[5] H. Heyer, Y. Katayama, S. Kawakami and K. Kawasaki, Extensions of finite commutative hypergroups, Sci. Math. Jpn. 65(3) (2007), 373-385.
[6] S. Oyanoki, Hypergroups associated with graphs, The 12th Mathematics Conference for Young Researches, 2015 (in Japanese).
[7] N. J. Wildberger, Hypergroups associated to random walks on the platonic solids, on the internet, 2016.
[8] M. Nihei, On the finite hypergroup associated with a strongly regular graph, Far East J. Math. Sci. (FJMS) 101(11) (2017), 2489-2498.
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