Bicyclic signed graphs with minimal and second minimal energy

Let S=(G,σ) be a signed graph of order n and size m, where G is its underlying graph and σ is the sign function. A connected signed graph S is said to be bicyclic if m=n+1. In this paper, we provide characterizations of bicyclic signed graphs with minimal and second minimal energy. We notice that there are gaps in the proofs of the main results in J. Zhang, H. Kan (2014) [32] and J. Zhang, B. Zhou (2005) [31] which deal with minimal energy of bicyclic graphs and we plug these gaps as a consequence of the results obtained for bicyclic signed graphs.