Unicyclic graphs with maximal energy Original Research Article

Let G be a graph on n vertices and let λ1,λ2,…,λn be its eigenvalues. The energy of G is defined as E(G)=λ1+λ2+cdots, three dots, centered+λn. For various classes of unicyclic graphs, the graphs with maximal energy are determined. Let Pn6 be obtained by connecting a vertex of the circuit C6 with a terminal vertex of the path Pn−6. For ngreater-or-equal, slanted7, Pn6 has the maximal energy among all connected unicyclic bipartite n-vertex graphs, except the circuit Cn.