m-Distance-regular graphs and their relation to multivariate P-polynomial association schemes - Archive ouverte HAL
Article Dans Une Revue Discrete Mathematics Année : 2024

m-Distance-regular graphs and their relation to multivariate P-polynomial association schemes

Résumé

An association scheme is P -polynomial if and only if it consists of the distance matrices of a distance-regular graph. Recently, bivariate P-polynomial association schemes of type (α, β) were introduced by Bernard et al., and multivariate P-polynomial association schemes were later defined by Bannai et al. In this paper, the notion of m-distance-regular graph is defined and shown to give a graph interpretation of the multivariate P -polynomial association schemes. Various examples are provided. Refined structures and additional constraints for multivariate P -polynomial association schemes and m-distance-regular graphs are also considered. In particular, bivariate P-polynomial schemes of type (α, β) are discussed, and their connection to 2-distance-regular graphs is established.
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Dates et versions

hal-04738410 , version 1 (15-10-2024)

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Pierre-Antoine Bernard, Nicolas Crampé, Luc Vinet, Meri Zaimi, Xiaohong Zhang. m-Distance-regular graphs and their relation to multivariate P-polynomial association schemes. Discrete Mathematics, 2024, 347 (12), pp.114179. ⟨10.1016/j.disc.2024.114179⟩. ⟨hal-04738410⟩
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