Some Applications Of Graph Spectra

In this thesis, we investigate the application of graph spectra on the energy and the properties of the adjacency matrix of graphs. In chapter two, the minimal energy graph for fully angular hexagonal chains is helical hexagonal chain. In chapter three, the iff conditions of the singularity of the adjacency matrix of interaction bicycle graphs is obtained, the result is deduced in the following way: we find all sub-graphs of G with exactly n vertices, then the singularity of A is obtained according to formula In chapterfour, we make some simple dissicutions to the corona of two graphs, let G₁ and G₂ be two graphs on disjoint sets of n and m vertices, respectively. The corona G₁ o G₂ of G₁ and G₂is defined as the graph obtained by taking one copy of G₁ and n copies ofG₂, and then joining the i-th vertex of G₁ to every vertex in the i-th copy ofG₂, We consider the rank of the adjacency matrix of the corona of two graphs for some classes. In particular, we study the corona when G₂is complete graph,complete bipartite graph,Petersen graph and CP(k) graph.