A G-design is called balanced if the degree of each vertex x is a constant. A G-design is called strongly balanced if for every i = 1, 2, ..., h, there exists a constant C-i such that dA(i)(x) = C-i for every vertex x, where As are the orbits of the automorphism group of G on its vertex-set and dA(2)(x) of a vertex is the number of blocks of containing x as an element of A(i). We say that a G-design is simply balanced if it is balanced, but not strongly balanced. In this paper we determine the spectrum of simply balanced and strongly balanced 4-kite designs.

Balanced and Strongly Balanced 4-Kite Designs

Gionfriddo M;MILAZZO, Lorenzo Maria Filippo
2013

Abstract

A G-design is called balanced if the degree of each vertex x is a constant. A G-design is called strongly balanced if for every i = 1, 2, ..., h, there exists a constant C-i such that dA(i)(x) = C-i for every vertex x, where As are the orbits of the automorphism group of G on its vertex-set and dA(2)(x) of a vertex is the number of blocks of containing x as an element of A(i). We say that a G-design is simply balanced if it is balanced, but not strongly balanced. In this paper we determine the spectrum of simply balanced and strongly balanced 4-kite designs.
G-design, 4-kite, balanced, strongly balanced
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/14738
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