Decomposition of complete graphs using graph labelings

Abstract

A decomposition of a graph K into a set of graphs G1G2 Gt is a partition E1 E2 Et of E K such that E) Gi for I 1 i t where E) denotes the edge induced subgraph induced by the subset of edges Ei of K If a graph K has a decomposition G1G2 Gt and if each graph Gi is isomorphic to a graph G, for i, 1 i t then we say the graph K has a G decomposition Similarly if a graph K has a decomposition G1 G2 Gt and for each I 1 i t, Gi is isomorphic to either a graph G or a graph H such that there exist at least one i and at least one j for i j i 4 j and 1 i j t with Gi G and Gj H then we say the graph K has a G H decomposition newline