Bell Graphs are Determined by their Laplacian Spectra


Ali Zeydi Abdian




A graph $G$ is said to be determined by the spectrum of its Laplacian spectrum (DLS, for short) if every graph with the same spectrum is isomorphic to $G$. An $\infty$-graph is a graph consisting of two cycles with just a vertex in common. Consider the coalescence of an $\infty$-graph and the star graph $K_{1,s}$, with respect to their unique maximum degree. We call this a bell graph. In this paper, we aim to prove that all bell graphs are DLS.