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Spectral study of alliances in graphs

Juan Alberto Rodríguez-Velazquez, Jose Maria Sigarreta Almira (2007)

Discussiones Mathematicae Graph Theory

In this paper we obtain several tight bounds on different types of alliance numbers of a graph, namely (global) defensive alliance number, global offensive alliance number and global dual alliance number. In particular, we investigate the relationship between the alliance numbers of a graph and its algebraic connectivity, its spectral radius, and its Laplacian spectral radius.

Spinors in braided geometry

Mićo Đurđević, Zbigniew Oziewicz (1996)

Banach Center Publications

Let V be a ℂ-space, σ E n d ( V 2 ) be a pre-braid operator and let F l i n ( V 2 , ) . This paper offers a sufficient condition on (σ,F) that there exists a Clifford algebra Cl(V,σ,F) as the Chevalley F-dependent deformation of an exterior algebra C l ( V , σ , 0 ) V ( σ ) . If σ σ - 1 and F is non-degenerate then F is not a σ-morphism in σ-braided monoidal category. A spinor representation as a left Cl(V,σ,F)-module is identified with an exterior algebra over F-isotropic ℂ-subspace of V. We give a sufficient condition on braid σ that the spinor representation...

SPR0 substitutions and families of algebraic Riccati equations

G. Fernández-Anaya, J. C. Martínez García, Vladimír Kučera, D. Aguilar George (2006)

Kybernetika

We study in this paper Algebraic Riccati Equations associated with single-input single-output linear time-invariant systems bounded in H -norm. Our study is focused in the characterization of families of Algebraic Riccati Equations in terms of strictly positive real (of zero relative degree) substitutions applied to the associated H -norm bounded system, each substitution characterizing then a particular member of the family. We also consider here Algebraic Riccati Equations associated with systems...

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