Ma J, Shi Y, Wang Z, Yue J. On Wiener polarity index of bicyclic networks.
Sci Rep 2016;
6:19066. [PMID:
26750820 PMCID:
PMC4707490 DOI:
10.1038/srep19066]
[Citation(s) in RCA: 63] [Impact Index Per Article: 7.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2015] [Accepted: 12/02/2015] [Indexed: 11/09/2022] Open
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.
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