On the geometric-arithmetic Estrada index of graphs

Abstract The Estrada index and geometric-arithmetic index are two representative topological indices, and have been extensively utilized in QSPR/QSAR research. In this paper, we construct the geometric-arithmetic Estrada index EEGA, which is defined as the sum of terms e σ k (1 ≤ k ≤ n), where σk are eigenvalues of the geometric-arithmetic matrix of an n-vertex graph G. First, we give some bounds for the geometric-arithmetic Estrada index, and characterize their corresponding extremal graphs. In addition, some connections between EEGA and the geometric-arithmetic energy of graphs ( E G A ) are determined.