2021/12/15 by Monu Kadyan, Bikash Bhattacharjya, Kadyan, Monu +1
Mathematics · Chemistry · #Graph theory and applications #Synthesis and Properties of Aromatic Compounds #Finite Group Theory Research
paper · pdf · doi:10.48550/arxiv.2112.08085
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.