Abstract
In this note we investigate how to use an initial portion of the intersection array of a distance-regular graph to give an upper bound for the diameter of the graph. We prove three new diameter bounds. Our bounds are tight for the Hamming d-cube, doubled Odd graphs, the Heawood graph, Tutte’s 8-cage and 12-cage, the generalized dodecagons of order (1, 3) and (1, 4), the Biggs-Smith graph, the Pappus graph, the Wells graph, and the dodecahedron.
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Acknowledgments
The authors thank the anonymous reviewers for helpful and constructive comments that contributed to improving the final version of the paper.
Safet Penjić acknowledges the financial support from the Slovenian Research Agency (research program P1-0285 and research project J1-1695).
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Neumaier, A., Penjić, S. On Bounding the Diameter of a Distance-Regular Graph. Combinatorica 42, 237–251 (2022). https://doi.org/10.1007/s00493-021-4619-1
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DOI: https://doi.org/10.1007/s00493-021-4619-1