Construction And Spectra Of Non-Regular Minimal Graphs

The number of distinct eigenvalues of the adjacency matrix of graph G is bounded below by d(G)+1, where d is the diameter of the graph. Graphs attaining this lower bound are known as minimal graphs. The spectrum of graph G, where G is a simple and undirected graph is the collection of different eigenvalues of the adjacency matrix with their multiplicities. This paper deals with the construction of non-regular minimal graphs, together with the study of their characteristic polynomial and spectra.