A new class of integral graphs constructed from the hypercube

Abstract

In this paper, we determine the set of all distinct eigenvalues of the line graph which is induced by the first and second layers of the hypercube Qn, n>3. We show that this graph has precisely five distinct eigenvalues and all of its eigenvalues are integers. The main tool which we use in our work, is the equitable partition method in algebraic graph theory. We show how we can find, by using this method, the set of all distinct eigenvalues of a class of particular graphs.