Constructing Cospectral Non-isomorphic Signed Bipartite Graphs.

Let S = (G, σ) be a signed graph, where σ is the sign function on the edges of the underlying graph G. It is widely recognized that the adjacency spectrum alone cannot uniquely determine a signed graph. Therefore, it is of great interest to identify whether there exist any cospectral, non-isomorphic signed graphs within a specific class of signed graphs. In a significant contribution, Godsil et al. demonstrated that two components of G₁ × G₂, where both G₁ and G₂ are connected bipartite graphs, are cospectral if and only if at the minimum one of G1 and G2 is balanced. In this paper, we first generalize Godsil’s result for two connected signed bipartite graphs S₁ and S₂. Furthermore, we will define partitioned tensor product of two signed bipartite graphs, which will enable us to generate multiple pairs of cospectral non-isomorphic signed bipartite graphs. [ABSTRACT FROM AUTHOR]