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01-06-2015 | Original Research | Issue 1-2/2015

Bipartite unicyclic graphs with large energies

Journal:: Journal of Applied Mathematics and Computing > Issue 1-2/2015

Authors:: Jianming Zhu, Ju Yang

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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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Title: Bipartite unicyclic graphs with large energies
Authors:: Jianming Zhu
Ju Yang
Publication date: 01-06-2015
DOI: https://doi.org/10.1007/s12190-014-0817-y
Publisher: Springer Berlin Heidelberg
Journal: Journal of Applied Mathematics and Computing
Issue 1-2/2015
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085

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