Abstract:  Let G be a simple connected graph. By assigning an orientation to each edge of G, we obtained an oriented graph G^{\sigma}. The skew energy E_{s}(G^{\sigma}) of an oriented graph G^\sigma is defined as the sum of the absolute eigenvalues of the skew adjacency matrix for G^\sigma. Let \mathcal{B}^\circ_{n} be the set of bicyclic graphs without even cycles having n vertices. The ordering of graphs in \mathcal{B}^\circ_{n} in terms of their minimal skew energies was considered. By  employing the integral formula of skew energy and knowledge of real analysis, we deduced the first threegraphs with minimal skew energies in \mathcal{B}^\circ_{n} for n\geq 156 and 155 \geq n\geq 12, respectively.

Key words: oriented graphs, bicyclic graphs, skew energy