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The Maximum Hosoya Index of Unicyclic Graphs with Diameter at Most Four

1,†, 1,†, 1,†, 2,†, 3,† and 4,5,6,*,†
School of Mathematics and Statistics, Central South University New Campus, Changsha 410083, China
School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China
Predictive Society and Data Analytics Lab Faculty of Information Technolgy and Communication Sciences, Tampere University, 33100 Tampere, Finland
School of Management, University of Applied Sciences Upper Austria, 4400 Steyr, Austria
Department of Biomedical Computer Science and Mechatronics UMIT, 6060 Hall in Tyrol, Austria
College of Articial Intelligence, Nankai University, Tianjin 300350, China
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Symmetry 2019, 11(8), 1034;
Received: 28 June 2019 / Revised: 6 August 2019 / Accepted: 6 August 2019 / Published: 9 August 2019
PDF [313 KB, uploaded 14 August 2019]


The Hosoya index of a graph is defined by the total number of the matchings of the graph. In this paper, we determine the maximum Hosoya index of unicyclic graphs with n vertices and diameter 3 or 4. Our results somewhat answer a question proposed by Wagner and Gutman in 2010 for unicyclic graphs with small diameter. View Full-Text
Keywords: Hosoya index; unicyclic graphs; diameter Hosoya index; unicyclic graphs; diameter

Figure 1

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Liu, W.; Ban, J.; Feng, L.; Cheng, T.; Emmert-Streib, F.; Dehmer, M. The Maximum Hosoya Index of Unicyclic Graphs with Diameter at Most Four. Symmetry 2019, 11, 1034.

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