Displaying similar documents to “A construction of large graphs of diameter two and given degree from Abelian lifts of dipoles”

Distances on the tropical line determined by two points

María Jesús de la Puente (2014)

Kybernetika

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Let p ' and q ' be points in ℝ n . Write p ' ∼ q ' if p ' - q ' is a multiple of ( 1 , ... , 1 ) . Two different points p and q in ℝ n / ∼ uniquely determine a tropical line L ( p , q ) passing through them and stable under small perturbations. This line is a balanced unrooted semi-labeled tree on n leaves. It is also a metric graph. If some representatives p ' and q ' of p and q are the first and second columns of some real normal idempotent order n matrix A , we prove that the tree L ( p , q ) is described by a matrix F , easily obtained from A . We also...

On the vanishing of Iwasawa invariants of absolutely abelian p-extensions

Gen Yamamoto (2000)

Acta Arithmetica

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1. Introduction. Let p be a prime number and ℤ p the ring of p-adic integers. Let k be a finite extension of the rational number field ℚ, k ∞ a ℤ p -extension of k, k n the nth layer of k ∞ / k , and A n the p-Sylow subgroup of the ideal class group of k n . Iwasawa proved the following well-known theorem about the order A n of A n : Theorem A (Iwasawa). Let k ∞ / k be a ℤ p -extension and A n the p-Sylow subgroup of the ideal class group of k n , where k n is the n th layer of k ∞ / k . Then there exist integers λ = λ ( k ∞ / k ) ≥ 0 , μ = μ ( k ∞ / k ) ≥ 0 , ν = ν ( k ∞ / k ) , and n₀ ≥ 0...

On automorphisms of digraphs without symmetric cycles

Piotr Wójcik (1996)

Commentationes Mathematicae Universitatis Carolinae

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A digraph is a symmetric cycle if it is symmetric and its underlying graph is a cycle. It is proved that if D is an asymmetric digraph not containing a symmetric cycle, then D remains asymmetric after removing some vertex. It is also showed that each digraph D without a symmetric cycle, whose underlying graph is connected, contains a vertex which is a common fixed point of all automorphisms of D .

Guidance properties of a cylindrical defocusing waveguide

Oldřich John, Charles A. Stuart (1994)

Commentationes Mathematicae Universitatis Carolinae

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We discuss the propagation of electromagnetic waves of a special form through an inhomogeneous isotropic medium which has a cylindrical symmetry and a nonlinear dielectric response. For the case where this response is of self-focusing type the problem is treated in [1]. Here we continue this study by dealing with a defocusing dielectric response. This tends to inhibit the guidance properties of the medium and so guidance can only be expected provided that the cylindrical stratification...

Some results on L Σ ( κ ) -spaces

Fidel Casarrubias Segura, Oleg Okunev, Paniagua C. G. Ramírez (2008)

Commentationes Mathematicae Universitatis Carolinae

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We present several results related to L Σ ( κ ) -spaces where κ is a finite cardinal or ω ; we consider products and some constructions that lead from spaces of these classes to other spaces of similar classes.