Minimal skew energy of oriented unicyclic graphs with a perfect matching

Jian-ming Zhu, Ju Yang
2014 Journal of Inequalities and Applications  
Let G σ be an oriented graph of a simple undirected graph G with an orientation σ , which assigns to each edge of G a direction so that the resultant graph G σ becomes a directed graph. The skew energy of G σ is defined as the sum of the absolute values of all eigenvalues of the skew-adjacency matrix of G σ . Denote by U σ (2k) the set of all oriented unicyclic graphs on 2k vertices with a perfect matching which contain no cycle of length l with l ≡ 2(mod 4). In this paper, we characterize the
more » ... riented graphs of U σ (2k) with the minimal skew energy for k ≥ 4. MSC: 05C50; 15A30
doi:10.1186/1029-242x-2014-486 fatcat:wqskrtvxpbb2timuyhdzznx3be