On the integral weighted oriented unicyclic graphs with minimum skew energy

In this paper, we investigate the minimal skew energies of integral weighted unicyclic oriented graphs, showing that the underlying graph of the oriented graph with minimum skew energy among all graphs over U(n,m)(n⩾6) is Sn,3, the graph obtained from a triangle by attaching n-3 pendent edges in exactly one of its vertices. Moreover, we show that its weight sequence has form(w1,a,a,…,a︷k,a+1,a+1,…,a+1︷n-3-k,w2,w3)in which the arc lying on the cycle C3 and incident to no pendent arcs has weight w1, and the two largest weights correspond the other two arcs of C3, where positive integer numbers w1,w2,w3,a and k satisfy 1⩽w1⩽a,a+1⩽w2⩽w3⩽a+w1 and m=w1+ka+(n-k-3)(a+1)+w2+w3. In addition, we determine the weight sequence above for n⩽m⩽3n-1.