The Wiener Polarity Index Of Cactus Graphs And Some Extreme Value Problems

Graph theory is a branch of mathematics, which mainly explores the structure properties and algebraic properties of graphs. The molecular topological indices of graphs are a kind of important graph invariants, which is a hot spot in the research in the graph theory.The thesis mainly investigates the Wiener polarity index of cactus graphs. For any cactus graph, we present a calculation formula for its Wiener polarity index. Moreover, we characterize, for several kinds of cactus graphs, the structures of graphs the Wiener polarity index of which attains the extreme value.The thesis is organized as follows. In Chapter1, we firstly introduce the back-ground of the Wiener polarity index, and some notions and notations used in this thesis, then we discuss some basic problems concerning the Wiener polarity index, and list the main results we obtain in this thesis. In Chapter2, we first compute the Wiener polarity index of cactus graph, and then we compute the Wiener polarity index of chain cactus. In Chapter3, we characterize the extreme graph of cactus graph with extreme value Wiener polarity index.