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On Generalized Strongly Regular Graphs

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Abstract

A generalized strongly regular graph of grade p, as a generalization of strongly regular graphs, is a regular graph such that the number of common neighbours of both any two adjacent vertices and any two non-adjacent vertices takes on p distinct values. In this paper, we study generalized strongly regular graphs of grade 2 and provide some inequalities for the eigenvalues of them. In particular, we investigate a special family of generalized strongly regular graphs of grade 2, i.e., semi-strongly regular graphs. We obtain a relation between the parameters and two inequalities for the eigenvalues of these graphs. We also present some constructions of generalized strongly regular graphs based on Cayley graphs, graph operations and association schemes, respectively.

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Acknowledgements

The authors would like to thank the referees and editors for their valuable suggestions which have helped improve this paper.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, 050024, Hebei, China

    Dongdong Jia, Landang Yuan & Gengsheng Zhang

  2. Hebei Key Laboratory of Computational Mathematics and Applications, Shijiazhuang, 050024, Hebei, China

    Gengsheng Zhang

Authors
  1. Dongdong Jia
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  2. Landang Yuan
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  3. Gengsheng Zhang
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Corresponding author

Correspondence to Gengsheng Zhang.

Additional information

This research is partially supported by National Natural Science Foundation of China (Grant No. 11571091), Natural Science Foundation of Hebei Education Department (Grant No. ZD2016096) and Natural Science Foundation of Hebei Normal University (Grant No. L2015Z02).

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Jia, D., Yuan, L. & Zhang, G. On Generalized Strongly Regular Graphs. Graphs and Combinatorics 34, 555–570 (2018). https://doi.org/10.1007/s00373-018-1894-8

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  • DOI: https://doi.org/10.1007/s00373-018-1894-8

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