Every Tree is a Subtree of a Graceful Unicyclic Graph: Graph Embedding

A decomposition of a graph K into a set of graphs {G1,G2,...,Gt} is a partition (E1,E2,...,Et) of E(K) such that ∼= Gi, for i,1 ≤ i ≤ t, where denotes the edge induced subgraph induced by the subset of edges Ei of K. If a graph K has a decomposition {G1,G2,...,Gt} and if each graph Giis 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 6= j and 1 ≤ i, j ≤ t with Gi∼= G and Gj∼= H, then we say the graph K has a (G,H)-decomposition. This book is pertaining to study G-decomposition of certain complete graphs, where G is a tree and (G,H)-decomposition of certain complete graphs, where G is a tree and H is either a path or a star or a cycle.