Bell Graphs are Determined by their Laplacian Spectra

Abstract

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 ∞-graph is a graph consisting of two cycles with just a vertex in common. Consider the coalescence of an ∞-graph and the star graph K1,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.