Abstract
In this paper, we consider the wreath product of two graphs that yields much more larger graphs than other graph products. We drive a formula for the adjacency spectrum of the wreath product of a complete graph and a circulant graph. As its applications, we obtain their (normalized) Laplacian spectra and further compute the adjacency spectra when the circulant graphs are respectively the Möbius ladder graph, the crown graph and the Andrásfai graph. Moreover, some known results are generalized and a problem is posed for further study.
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Acknowledgements
The first four authors are supported by National Natural Science Foundation of China (No. 11971247). The third author is also supported by Special Fund for Taishan Scholars Project. The fifth author is supported by Natural Science Foundation of **njiang (No. 2019D01B10) and Youth Doctoral Cultivation Project for Sci-Tech Talents of **njiang (No. 2018Q074). The authors also would like to thank the anonymous referee for his or her many valuable suggestions towards improving this paper.
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Li, X., Zhang, Y., Wang, J. et al. On the spectra of wreath products of circulant graphs. Ricerche mat (2023). https://doi.org/10.1007/s11587-023-00770-4
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DOI: https://doi.org/10.1007/s11587-023-00770-4