Abstract
A decomposition of a graph G is a family of edge-disjoint subgraphs {G1, G2,…, Gk} such that E(G) = E(G1) ∪ E(G2) ∪ … ∪ E(Gk). If each Gi is isomorphic to H for some subgraph H of G, then the decomposition is called a H -decomposition of G. In this paper, we give necessary and sufficient condition for the decomposition of the total graph of standard graphs and corona of graphs into paths on three edges.
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