Counterexamples to a conjecture of Dias on eigenvalues of chemical graphs

Abstract

Chemical graphs (simple, connected graphs with maximum degree no greater than three) with eigenvalues ±√ 8 exist for all orders greater than nine, disproving a conjecture of J.R. Dias that no chemical graph with this pair of eigenvalues exists. In fact, the eigenvalue pair can be achieved with arbitrarily high multiplicity.