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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,*,†
1
School of Mathematics and Statistics, Central South University New Campus, Changsha 410083, China
2
School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China
3
Predictive Society and Data Analytics Lab Faculty of Information Technolgy and Communication Sciences, Tampere University, 33100 Tampere, Finland
4
School of Management, University of Applied Sciences Upper Austria, 4400 Steyr, Austria
5
Department of Biomedical Computer Science and Mechatronics UMIT, 6060 Hall in Tyrol, Austria
6
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; https://doi.org/10.3390/sym11081034
Received: 28 June 2019 / Revised: 6 August 2019 / Accepted: 6 August 2019 / Published: 9 August 2019
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Abstract

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
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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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