5-regular oriented graphs with optimum skew energy

Abstract

Let G be a simple undirected graph and G σ be the corresponding oriented graph of G with the orientation σ. The skew energy of G σ , denoted by ε s (G σ ), is defined as the sum of the singular values of the skew adjacency matrix S(G σ ). In 2010, Adigawhere ∆ is the maximum degree of G of order n. In this paper, we determine all connected 5-regular oriented graphs of order n with maximum skew-energy.

Iota energy orderings of bicyclic signed digraphs

“…Thus the skew energy was defined as the sum of the absolute values of all eigenvalues of the skew adjacency matrix of an oriented graph. In 2017, Guo et al [16] determined all connected 5-regular oriented graphs with maximum skew-energy. In 2018, Deng et al [7] found all tournaments achieving the minimum skew energy.…”