The Elgenvalues Of Graph Transformations

The eigenvalues of a graph are eigenvalues of its adjacency matrix, where the laregest eigenvalue is called the index of the graph. In this papar, we mainly study how the eigenvalues and the index change after the graph transformations. There are three main sections: In chapter 2 we apply the characteristic polynomial and graph angles to study the eigenvalues; in chapter 3 we study the index by two lemmas (lemma 3.1 and lemma 3.6); hi chapter 4 we study the index of tricyclic Hamiltonian graphs with A(G) = 3 and determine the graph with maximal index.