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 C_i such that dA_i(x)= C_i for every vertex x, where A_iS are the orbits of the automorphism group of G on its vertex-set and d_Ai(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.