Some extremal properties of the resolvent energy, Estrada and resolvent Estrada indices of graphs.

Let G be a simple connected graph on n vertices and λ 1 , λ 2 , … , λ n be the eigenvalues of the adjacency matrix of G . Estrada and Higham proposed an invariant of a graph G based on Taylor series expansion of spectral moments E E ( G , c ) = ∑ k = 0 ∞ c k M k ( G ) . For c k = 1 n k (resp. 1 k ! , 1 ( n − 1 ) k ), E E ( G , c ) is the Resolvent energy (resp. Estrada index, Resolvent Estrada index) of G . In [18,17] , Gutman et al. conjectured the structure of the extremal members of some classes of graphs by the aid of computer on Resolvent energy and Resolvent Estrada index, respectively. In [1] , L. Allem et al. confirmed the validity of some of these conjectures on Resolvent energy. In this paper, we continue to study these indices based on these conjectures. [ABSTRACT FROM AUTHOR]