Abstract:
The eigenvalue of a graph G is the eigenvalue of its adjacency matrix. The energy E (G) of G is the sum of absolute values of its eigenvalues. A natural question arises: How the energy of a given graph G can be related with the graph obtained from G by means of some graph operations? In order to answer this question, we have considered two graphs namely, splitting graph S′(G) and shadow graph D2 (G). It has been proven that E (S′(G))=√ 5 E (G) and E (D2 (G))= 2E (G).
