Speaker
Description
Signed graphs provide a natural framework for modeling systems with antagonistic or cooperative interactions and arise in areas such as network science, social dynamics, and quantum systems. A signed graph $\Sigma = (G,\sigma)$ consists of an underlying graph $G = (V,E)$ together with a signature $\sigma : E \to \{+,-\}$.
In this talk, we present a new perspective on the Cartesian product of a path graph with an arbitrary signed graph $\Sigma$. Using tools from spectral graph theory and linear algebra, we derive explicit descriptions of the adjacency spectrum and Laplacian spectrum of the resulting Cartesian product in terms of the corresponding spectra of $\Sigma$.
We further establish sharp upper and lower bounds for the adjacency and Laplacian energies of these product graphs. As applications of our results, we construct infinite families of pairwise cospectral and Laplacian-cospectral signed graphs and compute the adjacency and Laplacian spectra for several well-known classes of graphs. These results contribute to the understanding of how spectral properties of signed graphs behave under graph products and transformations, and they highlight the role of spectral techniques in studying structural and energetic properties of signed networks, with potential relevance to graph learning and quantum network models.