The Unimodality Of Independence Polynomials Of Some Graphs

The research of independent sets of graph is one of the most original problems in graph theory. Some classical problems of graph theory are all indiscerptible with independent sets (for example, a matching of graph is a independent set of its line graph, and a clique of graph is a independent set of its complement graph). Independent sets of graph appear in the field of Coding, computer science theory and network theory. Thus, the research of independent sets of graph is highly active. Some scholars, Erdos and Moser, had embedded researched.The thesis mainly discuss the unimodality of independence polynomials of some graphs. It is divided four chapters.The first of which introduces basic concepts of graph and unimodality.The second chapter mainly verifies the LM conjecture: The independence polynomials of centipedes have only real zeros.The third chapter further investigates the unimodality of independence polynomials of caterpillars and vertebrates.The forth chapter mainly discusses the mode of independence polynomials of a class of graphs.