BALANCED AND STRONGLY BALANCED FRIENDSHIP GRAPH SYSTEMS
A friendship graph is the graph consisting of n3-cycles, having exactly one vertex in common. A friendship graph system of order vis a pair where Xis a finite set of vvertices and
is a collection of edge disjoint friendship graphs (called blocks) which partitions the edge set of the complete graph defined in the set X. A friendship graph system is called balanced if the number of blocks containing any given vertex in Xis a constant. A friendship graph system is called strongly balanced if for every there exists a constant such that for every vertex x, where are the orbits of the automorphism group of the friendship graph on its vertex set and of a vertex is the number of blocks of containing xas an element of In this paper, we determine the spectrum of balanced and strongly balanced friendship graph systems.
balanced, strongly balanced, simply balanced, friendship graph, butterfly.