Balanced and strongly balanced (m, n)-tadpole systems

Abstract

An (m, n)-tadpole system of order v is a pair E = (X, B), where X is the vertex set of the complete graph K_v and B is a collection of edge disjoint (m,n)-tadpoles which partitions the edge set of K_v. In this paper, the balanced and strongly balanced (3,2) and (4,2)-tadpole systems are studied. Furthermore, we determine the spectrum of those tadpole systems which are balanced, but not strongly balanced. © 2018 Utilitas Mathematica Publishing Inc. All rights reserved.