On the spectrum of a ring-structured directed graph's adjacency matrix and its application

In the paper, it was investigated that if 2 arcs were removed from ring-structured directed graph with 2 Hamilton circuits, its spectrum would remain real if and only if the number of nodes were even, and the “distance between the arcs” removed from one cyclic path were maximal. The applicability of the results to fault-tolerance estimation of ring topology networks is examined.