Unicyclic signed graphs with the first ⌊n+12⌋ largest energies

Abstract Let x 1 , x 2 , … , x n be the eigenvalues of a signed graph S of order n . The energy of S is defined as E ( S ) = ∑ i = 1 n | x i | . In this paper, we show the integral formula on the difference of the energies of two bipartite signed graphs with the same order and present a new technique of directly comparing the energies of two subdivision bipartite signed graphs. As applications, we can characterize the unicyclic signed graphs of order n with the first largest to the ⌊ n + 1 2 ⌋ t h largest energies for n ≥ 88 .