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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