Resolvent Estrada Index - Computational and Mathematical Studies

The resolvent Estrada index of a (non-complete) graph G of order n is defined as EEr = ∑n i=1 ( 1− λi n−1 )−1 , where λ1, λ2, . . . , λn are the eigenvalues of G. Combining computational and mathematical approaches, we establish a number of properties of EEr . In particular, any tree has smaller EEr-value than any unicyclic graph of the same order, and any unicyclic graph has smaller EEr-value than any tricyclic graph of the same order. The trees, unicyclic, bicyclic, and tricyclic graphs with smallest and greatest EEr are determined.

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