Bicyclic signed graphs with at most one odd cycle and maximal energy

Abstract Let x 1 , x 2 , … , x n be the eigenvalues of a signed graph Γ of order n . The energy of Γ is defined as E ( Γ ) = ∑ j = 1 n | x j | . Let P n 4 , 4 be the signed graph obtained from two copies of negative cycles ( C 4 , σ ¯ ) joined by a path P n − 6 . In this paper, we show that P n 4 , 4 has the maximal energy among all n -vertices connected bicyclic signed graphs with at most one odd cycle.