On the Skew Spectra of Cartesian Products of Graphs (original) (raw)

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Keywords: Oriented graphs, Spectra, Pfaffian graph

Abstract

An oriented graph Gsigma{G^{\sigma}}Gsigma is a simple undirected graph GGG with an orientation, which assigns to each edge of GGG a direction so that Gsigma{G^{\sigma}}Gsigma becomes a directed graph. GGG is called the underlying graph of Gsigma{G^{\sigma}}Gsigma and we denote by S(Gsigma)S({G^{\sigma}})S(Gsigma) the skew-adjacency matrix of Gsigma{G^{\sigma}}Gsigma and its spectrum Sp(Gsigma)Sp({G^{\sigma}})Sp(Gsigma) is called the skew-spectrum of Gsigma{G^{\sigma}}Gsigma. In this paper, the skew spectra of two orientations of the Cartesian products are discussed, as applications, new families of oriented bipartite graphs Gsigma{G^{\sigma}}Gsigma with Sp(Gsigma)=bfiSp(G)Sp({G^{\sigma}})={\bf i} Sp(G)Sp(Gsigma)=bfiSp(G) are given and the orientation of a product graph with maximum skew energy is obtained.

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How to Cite

Denglan, C., & Yaoping, H. (2013). On the Skew Spectra of Cartesian Products of Graphs. The Electronic Journal of Combinatorics, 20(2), #P19. https://doi.org/10.37236/2864