Skew Spectrum of the Cartesian Product of an Oriented Graph with an Oriented Hypercube

A. Anuradha () and R. Balakrishnan ()
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A. Anuradha: Bharathidasan University, Department of Mathematics
R. Balakrishnan: Bharathidasan University, Department of Mathematics

A chapter in Combinatorial Matrix Theory and Generalized Inverses of Matrices, 2013, pp 1-12 from Springer

Abstract: Abstract Let σ be an orientation of a simple graph H yielding an oriented graph H σ . We define an orientation ψ to the Cartesian product G=H□Q d of H with the hypercube Q d by orienting the edges of G in a specific way. The skew adjacency matrices S(G ψ ) obtained in this way for some special families of G answer some special cases of the Inverse Eigenvalue Problem. Further we present a new orientation ϕ to the hypercube Q d for which the skew energy equals the energy of the underlying hypercube, distinct from the two orientations of hypercubes defined by Tian (Linear Algebra Appl. 435:2140–2149, 2011) and show how one of the two orientations of Q d described by Tian is a special case of our method.

Keywords: Oriented graph; Oriented hypercubes; Spectrum of graph; Skew spectrum; 05C50 (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-81-322-1053-5_1

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DOI: 10.1007/978-81-322-1053-5_1

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