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Abstract
The number of spanning trees of a graph G is the total number of distinct spanning subgraphs of G that are trees. In this paper, we present sharp upper bounds for the number of spanning trees of a graph with given matching number.
Acknowledgments
The authors are much grateful to two anonymous referees for their careful reading, constructive corrections and valuable comments on our paper, which have considerably improved the presentation of this paper.
Disclosure statement
No potential conflict of interest was reported by the authors.
Additional information
Funding
Supported by NNSFC (Nos. 11101245, 11271208, 11301302, 11201227), NSF of Shandong (No. BS2013SF009), China Postdoctoral Science Foundation (Nos. 2013M530869, 2014T70210), Mathematics and Interdisciplinary Sciences Project of Central South University Foundation for Youth in SDIBT (2013QN056), Natural Science Foundation of Jiangsu Province (BK20131357), National Research Foundation funded by the Korean government with the grant no. [2013R1A1A2009341].