On The Spectral Radius Of Two Types Of Graphs

The spectral theory of graph is not only an important area in graph theory but also an active topic. There are extensive applications in the fields of quantum chemistry, physics, computer science, communication network and information science. The theory of graphs and relations between the spectra and fixed variate (e.g. chromatic number, degree sequence, diameter and connectivity) of graphs by means of the well-developed theory and technique of algebra, topological structure properties of graph, combination and matrix theories so as to establish firm essential relation between the algebraic properties and topological properties of graphs and networks.In this paper, we mainly study the adjacency spectrum of simple connected undirected graphs. Some results will be given in this thesis.1. By using the improved method of graft transformation, the sharp upper bound on the spectral radius the Nordhaus-Gaddum type at trees is given. We show thatρ(T) + ρ(T^c) ≤ (n-1)^1/2 + n － 2,the equality holds if and only if T (?) K_1,(n－1).2. We study the tree with diameter 3. We prove that the spectral radius of the Nordhaus-Gaddum type for double-star S(a, b) is strictly increasing in variable a, where [(n－1)/2] ≤ a ≤ n － 3.3. We study the spectral radius of graphs with k cut edges, and the...