Spectral characterizations of signed cycles (vol 553, pg 307, 2018)

A signed graph is a pair, say (G, sigma), where G is the underlying graph and sigma : E(G) -> {-1 ,+1} is a sign function on the edges of G. In this paper we present the complete characterization of cospectral mates of negative even cycles, that is the signed even cycles with only one negative edge. In [Spectral characterizations of signed cycles, Linear Algebra Appl. 553 (2018) 307-327], the authors characterized the cospectral mates of negative even cycles but they missed a few of them. Here, we characterize all cospectral mates of negative even cycles. (c) 2022 Elsevier Inc. All rights reserved.

Automated summary

A signed graph consists of an underlying graph and a sign function on its edges. This paper presents the complete characterization of cospectral mates of negative even cycles, which are signed even cycles with only one negative edge. The authors of a previous study partially characterized the cospectral mates of negative even cycles, but this paper provides the complete characterization.