On connected signed graphs with rank equal to girth

Let Γ=(G,σ) be a signed graph. The rank of Γ is the rank of the adjacency matrix of Γ. If the underlying graph G of Γ has at least one cycle, then the girth of Γ, denoted by gr(Γ), is the length of the shortest cycle in G. Zhou et al. (2021) [35] have identified connected graphs G with rank equal to gr(G) (or gr(G)−2). In this paper, we extend their work to the setting of signed graphs.