Li, Weiqiang2016-04-262016-04-262015http://udspace.udel.edu/handle/19716/17682The algebraic methods have been very successful in understanding the structural properties of graphs. In general, we can use the eigenvalues of the adjacency matrix of a graph to study various properties of graphs. In this thesis, we obtain the whole spectrum of a family of graphs called Wenger graphs Wm (q ). We also study the a conjecture of Brouwer, concerning the second connectivity of strongly regular graphs. Finally, we compute the extendability of matchings for many strongly regular graphs and many distance-regular graphs.Graph theory.Algebra.Graph connectivity.Brouwer, A. E. -- (Andries Evert)Thesis947837861