Minimal Skew energy of oriented bicyclic graphs with a given diameter

Let $S(G^σ)$ be the skew-adjacency matrix of the oriented graph $G^σ$, which is obtained from a simple undirected graph $G$ by assigning an orientation $σ$ to each of its edges. The skew energy of an oriented graph $G^σ$ is defined as the sum of absolute values of all eigenvalues of $S(G^σ)$. For any positive integer $d$ with $3\leq d\leq n-3$, we determine the graph with minimal skew energy among all oriented bicyclic graphs that contain no vertex disjoint odd cycle of lengths $s$ and $l$ with $s+l\equiv 2(mod 4)$ on $n$ vertices with a given diameter $d$.

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