algebraic Graph Theory - Monu Kadyan

Title: Four types of integrality on mixed Cayley graphs over abelian groups

Abstract: A mixed graph is called H-integral (resp. HS-integral) if the eigenvalues of its Hermitian-adjacency matrix (resp. Hermitian-adjacency matrix of second kind) are integers. Similarly,  a mixed graph is said to be Gaussian integral (resp. Eisenstein integral) if the eigenvalues of its (0,1)-adjacency matrix are Gaussian integers (resp. Eisenstein integers). In this talk, I will present a characterization of H-integrality, HS-integrality, Gaussian integrality, and Eisenstein integrality on mixed Cayley graphs over abelian groups. This is joint work with Bikash Bhattacharjya.