We prove that, for any graph G, its energy is at least twice the Randic index. show that equality holds if and only G union of complete bipartite graphs.

Let G be a finite connected simple graph and μ(G) be the Mycielskian of G. We show that for connected graphs G and H, μ(G) is isomorphic to μ(H) if and only if G is isomorphic to H. Furthermore, we determine the energy of the Mycielskian of a connected regular graph G in terms of the energy E(G) of G, where the energy of G is the sum of the absolute values of the eigenvalues of G. The energy of...

The energy of a graph G, often denoted E(G), is defined to be the sum of the absolute value of the eigenvalues of its adjacency matrix. This graph invariant is very closely connected to a chemical quantity known as the total π-electron energy of conjugated hydrocarbon molecules. Very recently graph energy has become a quantity of interest to mathematicians, and several variations have been intr...

The skew energy of an oriented graph was introduced by Adiga, Balakrishnan and So in 2010, as one of various generalizations of the energy of an undirected graph. Let G be a simple undirected graph, and Gσ be an oriented graph of G with the orientation σ and skew-adjacency matrix S(Gσ). The skew energy of the oriented graph Gσ , denoted by ES(G), is defined as the sum of the norms of all the ei...