Skew-spectra and skew energy of various products of graphs

2013/05/31 by Xueliang Li, Li, Xueliang, Huishu Lian +1
Computer Science · Mathematics · #05C20 #05C50 #05C90 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.1305.7305

openalex publication_date 2013/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a graph G, let G^σ be an oriented graph of G with the orientation σ and skew-adjacency matrix S(G^σ). Then the spectrum of S(G^σ) consisting of all the eigenvalues of S(G^σ) is called the skew-spectrum of G^σ, denoted by Sp(G^σ). The skew energy of the oriented graph G^σ, denoted by E_S(G^σ), is defined as the sum of the norms of all the eigenvalues of S(G^σ). In this paper, we give orientations of the Kronecker product H⊗ G and the strong product H∗ G of H and G where H is a bipartite graph and G is an arbitrary graph. Then we determine the skew-spectra of the resultant oriented graphs. As applications, we construct new families of oriented graphs with maximum skew energy. Moreover, we consider the skew energy of the orientation of the lexicographic product H[G] of a bipartite graph H and a graph G.

Citations

• A survey on the skew energy of oriented graphs
• 4-Regular oriented graphs with optimum skew energy

Related

• A survey on the skew energy of oriented graphs
• More on the skew-spectra of bipartite graphs and Cartesian products of graphs
• Oriented unicyclic graphs with extremal skew energy
• The skew energy of random oriented graphs
• On oriented graphs with minimal skew energy