title: On Wiener polarity index of bicyclic networks.
abstract: Complex networks are ubiquitous in biological, physical and social sciences. Network robustness research aims at finding a measure to quantify network robustness. A number of Wiener type indices have recently been incorporated as distance-based descriptors of complex networks. Wiener type indices are known to depend both on the network's number of nodes and topology. The Wiener polarity index is also related to the cluster coefficient of networks. In this paper, based on some graph transformations, we determine the sharp upper bound of the Wiener polarity index among all bicyclic networks. These bounds help to understand the underlying quantitative graph measures in depth.
authors.affiliation: Center for Combinatorics and LPMC-TJKLC, Nankai University, Tianjin, 300071, China.
authors.forename: Jing
authors.initials: J
authors.lastname: Ma
authors.affiliation: Center for Combinatorics and LPMC-TJKLC, Nankai University, Tianjin, 300071, China.
authors.forename: Yongtang
authors.initials: Y
authors.lastname: Shi
authors.affiliation: Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga-koen, Kasugashi, Fukuoka, Japan.
authors.forename: Zhen
authors.initials: Z
authors.lastname: Wang
authors.affiliation: School of Mathematical Sciences, Shandong Normal University, Jinan 250014, Shandong, China.
authors.forename: Jun
authors.initials: J
authors.lastname: Yue