Wiener Polarity Index and Its Generalization in Trees

作者：Lei, Hui; Li, Tao; Shi, Yongtang^*; Wang, Hua

来源：MATCH-Communications in Mathematical and in Computer Chemistry, 2017, 78(1): 199-212.

• UNICYCLIC GRAPHS
• RANDIC INDEX
• BICYCLIC GRAPHS
• DEGREE SEQUENCE
• NUMBER
• EDGES
• SUBGRAPHS
• DIAMETER
• DISTANCE
• PATHS

The Wiener polarity index of a graph G, denoted by W-p(G), is defined as the number of unordered pairs of vertices that are at distance 3 in G. As one of the classic topological indices, properties of W-p(G) have been extensively studied for various graphs in the recent years. In this note we limit our attention to trees. First we characterize the extremal trees with given degree sequence with respect to the Wiener polarity index. Then we compare the extremal trees with different degree sequences. As a result, extremal statements on the Wiener polarity index of different families of trees follow as immediate consequences. We also briefly discuss the generalization of the Wiener polarity index.

• 出版日期2017
• 单位南开大学