Minimal skew energy of oriented unicyclic graphs with a perfect matching

Abstract

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 oriented graphs of U σ (2k) with the minimal skew energy for k ≥ 4. MSC: 05C50; 15A30

Minimal Skew energy of oriented bicyclic graphs with a given diameter

“…For the oriented bicyclic graphs, Shen et al [11] deduced the oriented graphs with the minimal and maximal skew energies, and Wang et al [13] characterized the oriented graph with the second largest skew energy. Zhu and Yang [19] obtained the oriented unicyclic graphs that have perfect matchings with the minimal skew energy. Yang et al [15] determined the oriented unicyclic graphs of a fixed diameter with the minimal skew energy.…”