HS-integral and Eisenstein integral mixed circulant graphs

Authors

Monu Kadyan, Indian Institute of Technology GuwahatiFollow
Bikash Bhattacharjya, Indian Institute of Technology GuwahatiFollow

Abstract

A mixed graph is called second kind hermitian integral (HS-integral) if the eigenvalues of its Hermitian-adjacency matrix of the second kind are integers. A mixed graph is called Eisenstein integral if the eigenvalues of its (0, 1)-adjacency matrix are Eisenstein integers. We characterize the set S for which a mixed circulant graph Circ(Z_n, S) is HS-integral. We also show that a mixed circulant graph is Eisenstein integral if and only if it is HS-integral. Further, we express the eigenvalues and the HS-eigenvalues of unitary oriented circulant graphs in terms of generalized Möbius function.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

Recommended Citation

Kadyan, Monu and Bhattacharjya, Bikash (2023) "HS-integral and Eisenstein integral mixed circulant graphs," Theory and Applications of Graphs: Vol. 10: Iss. 1, Article 3.
DOI: 10.20429/tag.2023.100103
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol10/iss1/3