Given a graph $G$, let $G^\sigma$ be an oriented graph of $G$ with the orientation $\sigma$ and skew-adjacency matrix $S(G^\sigma)$. Then the spectrum of $S(G^\sigma)$ consisting of all the eigenvalues of $S(G^\sigma)$ is called the skew-spectrum of $G^\sigma$, denoted by $Sp(G^\sigma)$. The skew energy of the oriented graph $G^\sigma$, denoted by $\mathcal{E}_S(G^\sigma)$, is defined as the sum of the norms of all the eigenvalues of $S(G^\sigma)$. In this paper, we give orientations of the Kronecker product $H\otimes G$ and the strong product $H\ast G$ 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 optimum 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 $G$.
Li, X. and Lian, H. (2015). Skew-spectra and skew energy of various products of graphs. Transactions on Combinatorics, 4(2), 13-21. doi: 10.22108/toc.2015.6417
MLA
Li, X. , and Lian, H. . "Skew-spectra and skew energy of various products of graphs", Transactions on Combinatorics, 4, 2, 2015, 13-21. doi: 10.22108/toc.2015.6417
HARVARD
Li, X., Lian, H. (2015). 'Skew-spectra and skew energy of various products of graphs', Transactions on Combinatorics, 4(2), pp. 13-21. doi: 10.22108/toc.2015.6417
CHICAGO
X. Li and H. Lian, "Skew-spectra and skew energy of various products of graphs," Transactions on Combinatorics, 4 2 (2015): 13-21, doi: 10.22108/toc.2015.6417
VANCOUVER
Li, X., Lian, H. Skew-spectra and skew energy of various products of graphs. Transactions on Combinatorics, 2015; 4(2): 13-21. doi: 10.22108/toc.2015.6417
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