An edge grafting theorem on the energy of unicyclic and bipartite graphs

The energy of a graph is the sum of the absolute values of the eigenvalues of its adjacency matrix. The edge grafting operation on a graph is certain kind of edge moving between two pendant paths starting from the same vertex. In this paper we show how the graph energy changes under the edge grafting operations on unicyclic and bipartite graphs. We also give some applications of this result on the comparison of graph energies between unicyclic or bipartite graphs.