Eigenvalues of Cayley graphs. (English) Zbl 1492.05093

Liu, Xiaogang; Zhou, Sanming

Electron. J. Comb. 29, No. 2, Research Paper P2.9, 164 p. (2022).

This is a survey comprising the main results on eigenvalues of Cayley graphs, digraphs, distinct generalizations, and their applications.
The text is divided into 14 chapters: Introduction; Eigenvalues of Cayley graphs; Integral Cayley graphs; Cospectral Cayley graphs; Cayley graphs on finite rings; Energies of Cayley graphs; Ramanujan Cayley graphs; Second largest eigenvalue of Cayley graphs; Perfect state transfer in Cayley graphs; Distance-regular Cayley graphs; Generalizations of Cayley graphs; Directed Cayley graphs; Miscellaneous; Open problems and research topics.
The bibliography is quite interesting and contains 394 references.

Reviewer: Carlos M. da Fonseca (Safat)

MSC:

05C50	Graphs and linear algebra (matrices, eigenvalues, etc.)
05C25	Graphs and abstract algebra (groups, rings, fields, etc.)

Keywords:

Cayley Graphs; eigenvalues

Software:

GAP

References:

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