Unicyclic graphs with maximal energy

Unicyclic graphs with maximal energy

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| + · · · + |λn|. For various classes of unicyclic graphs, the graphs with maximal energy are determined. Let P 6 n be obtained by connecting a vertex of the circuit C6 with a terminal vertex of the path Pn−6. For n 7, P 6 n has the maximal energy among all connected unic...

Unicyclic Graphs with equal Laplacian Energy

We introduce a new operation on a class of graphs with the property that the Laplacian eigenvalues of the input and output graphs are related. Based on this operation, we obtain a family of Θ( √ n) noncospectral unicyclic graphs on n vertices with the same Laplacian energy.

Unicyclic radially-maximal graphs on the minimum number of vertices

We characterize unicyclic, non-selfcentric, radially-maximal graphs on the minimum number of vertices. Such graphs must have radius r ≥ 5, and we prove that the number of these graphs is 1 48 r + O(r).

Graphs and matrices with maximal energy

Given a complex m n matrix A; we index its singular values as 1 (A) 2 (A) ::: and call the value E (A) = 1 (A)+ 2 (A)+ ::: the energy of A; thereby extending the concept of graph energy, introduced by Gutman. Koolen and Moulton proved that E (G) (n=2) (1 + p n) for any graph G of order n and exhibited an in…nite family of graphs with E (G) = (v (G) =2) 1 + p v (G) . We prove that for all su¢ ci...

Regular graphs with maximal energy per vertex