Graph theory analyses of polymers

Abstract

In this chapter, we introduce graph theory for analyzing structures of multicyclic polymers. An essential graph theory reference is [1].

In Section 2.1, we introduce basic concepts of graphs in which we define a polymer graph that represents a polymer structure. In Section 2.2, we introduce a systematic notation of polymer structure by using their graphs. This nomenclature and its application are the main themes of this chapter. In Section 2.3, we enumerate multicyclic polymers using the notation. Figures of graphs with rank 4 at most are discussed here. In Section 2.4, we discuss an application of L. Euler’s solution of the K¨onigsberg bridge problem.We introduce the folding operation and characterize what graph can be obtained from a simple linear graph by folding. As an application, we discuss the characterization of multicyclic polymers obtained from a simple linear graph by folding.