Three Types of Edge-Switchable Kite Systems

Abstract

Informally, a \(\epsilon\)-switchable \(G\)-design is a decomposition of the complete graph into subgraphs of isomorphic copies of \(G\) which have the property that they remain a \(G\)-decomposition when \(\epsilon\)-edge switches are made to the subgraphs. This paper determines the spectrum of \(\epsilon\)-switchable \(G\)-designs where \(G\) is a kite (a triangle with an edge attached) and \(\epsilon\) takes \(t\)-edge, \(h\)-edge, and \(l\)-edge.