Geodesic
Characteristic polynomials of skew-adjacency matrices of oriented graphs
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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An oriented graph $\overleftarrow{G}$ is a simple undirected graph $G$ with an orientation, which assigns to each edge a direction so that $\overleftarrow{G}$ becomes a directed graph. $G$ is called the underlying graph of $\overleftarrow{G}$ and we denote by $S(\overleftarrow{G})$ the skew-adjacency matrix of $\overleftarrow{G}$ and its spectrum $Sp(\overleftarrow{G})$ is called the skew-spectrum of $\overleftarrow{G}$. In this paper, the coefficients of the characteristic polynomial of the skew-adjacency matrix $S(\overleftarrow{G}) $ are given in terms of $\overleftarrow{G}$ and as its applications, new combinatorial proofs of known results are obtained and new families of oriented bipartite graphs $\overleftarrow{G}$ with $Sp(\overleftarrow{G})={\bf i} Sp(G) $ are given.
DOI : 10.37236/643
Classification : 05C20, 05C50
Mots-clés : skew-energy, skew-spektrum, skew-adjacency matrix, digraph, oriented graph 
@article{10_37236_643,
     author = {Yaoping Hou and Tiangang Lei},
     title = {Characteristic polynomials of skew-adjacency matrices of oriented graphs},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/643},
     zbl = {1236.05093},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/643/}
}
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Yaoping Hou; Tiangang Lei. Characteristic polynomials of skew-adjacency matrices of oriented graphs. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/643

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