2021/12/15 by Monu Kadyan, Bikash Bhattacharjya, Kadyan, Monu +1 · 1 citation
Chemistry · Mathematics · #Finite Group Theory Research #Graph theory and applications #Synthesis and Properties of Aromatic Compounds #math.CO #msc:05C25 #msc:05C50
paper · pdf · doi:10.48550/arxiv.2112.08085
arXiv admin note: text overlap with arXiv:2106.01261
arxiv created 2022/06/22 · arxiv updated 2022/06/23
A mixed graph is called second kind hermitian integral(or HS-integral) if the eigenvalues of its Hermitian-adjacency matrix of 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(ℤn, S) is HS-integral. We also show that a mixed circulant graph is Eisenstein integral if and only if it is HS-integral. Further, the eigenvalues and the HS-eigenvalues of some oriented circulant graphs are expressed in terms of generalized Mobius function.