Integral graphs

Abstract

A graph is called integral if all the eigenvalues of its adjacency matrix are integers. In this thesis, we define some graph operations which when applied on integral graphs generate other integral graphs. Also we present the relationship between integral trees of diameter 3 and Pell's equation and give a new theorem on its generalisation for constructing infinite families of integral trees of diameter 3. Furthermore, we present some characterisation of families of integral trees with even diameter and odd diameter.