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On the distance eigenvalues of design graphs

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Abstract

A design graph is a regular bipartite graph in which any two distinct vertices of the same part have the same number of common neighbors. This class of graphs has a close relationship to strongly regular graphs. In this paper, we study the distance eigenvalues of the design graphs. Also, we will explicitly determine the distance eigenvalues of a class of design graphs, and determine the values for which the class is distance integral, that is, its distance eigenvalues are integers.

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Acknowledgements

The author is thankful to the anonymous reviewers for their valuable comments and suggestions.

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  1. Department of Mathematics, Faculty of Basic Sciences, Lorestan University, Khorramabad, Iran

    S. Morteza Mirafzal

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  1. S. Morteza Mirafzal
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Correspondence to S. Morteza Mirafzal.

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Mirafzal, S.M. On the distance eigenvalues of design graphs. Ricerche mat 73, 2759–2769 (2024). https://doi.org/10.1007/s11587-023-00794-w

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  • DOI: https://doi.org/10.1007/s11587-023-00794-w

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