Abstract
The energy of a graph is defined as the sum of the absolute values of the eigenvalues of its adjacency matrix. In this paper, we present a new technique to compare the energies of two bipartite graphs whose characteristic polynomials satisfy a given recurrence relation. As its applications, we can characterize the bipartite unicyclic graphs of order \(n\) with maximal, second-maximal, and third-maximal energy for \(n\ge 27\), and thus confirm the validity of the results in (Gutman et al. MATCH Commun Math Comput Chem 58:75–82, 2007) which were obtained by numerical calculations.
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Acknowledgments
The first author is very grateful to Professor Jia-Yu Shao for his help. We also sincerely thank the anonymous referees for the valuable comments. This work is supported by Shanghai Project 085, National Natural Science Foundation of China (No. 71173145), “Shu Guang” project(11SG53) and Shanghai Municipal Education Commission key discipline (J51201).
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Zhu, J., Yang, J. Bipartite unicyclic graphs with large energies. J. Appl. Math. Comput. 48, 533–552 (2015). https://doi.org/10.1007/s12190-014-0817-y
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DOI: https://doi.org/10.1007/s12190-014-0817-y