Maximum degree Estrada index

Abstract

The Estrada index is one of the most well-known topological graph indices due to its chemical and biological applications. It has close relation with the spectrum of the graph and with spectral moments. A recent related topic is the maximum degree matrix. In this paper, the maximum degree Estrada index MEE is defined as the sum of the exponentials of the eigenvalues of the maximum degree matrix and its properties are studied. Upper and lower bounds in terms of energy and several graph parameters are obtained for MEE. MEE is also calculated for some well-known graph classes. The MEE of cycle and path graphs are obtained in terms of the Bessel function and cosh function. Exact and approximated values of the MEE(Pn) and MEE(Cn) are listed as a table.