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Published in:
2013 | OriginalPaper | Chapter
Skew Spectrum of the Cartesian Product of an Oriented Graph with an Oriented Hypercube
Authors : A. Anuradha, R. Balakrishnan
Published in: Combinatorial Matrix Theory and Generalized Inverses of Matrices
Publisher: Springer India
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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.