Balanced and strongly balanced 4-kite designs

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 Ci such that dAi(x)= Ci for every vertex x, where AiS are the orbits of the automorphism group of G on its vertex-set and dAi(x) of a vertex is the number of blocks of containing x as an element of Ai. 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.