Abstract
Let be the group of fourth roots of unit. A
-gain graph is a graph where each orientation of an edge is given a complex unit in
, which is the inverse of the complex unit assigned to the opposite orientation. In this paper, we characterize the structure of the
-gain graphs with exactly one positive eigenvalue and determine the
-gain graphs with cut vertices having exactly two positive eigenvalues. Our results extend some parallel ones about mixed graphs and signed graphs.
AMS SUBJECT CLASSIFICATION:
Acknowledgments
The authors are so grateful to the referee for their valuable comments and corrections which improve the presentation of the paper.
Disclosure statement
No potential conflict of interest was reported by the author(s).