Bounds on α-distance Randić Estrada index

In this paper, for a simple undirected connected graph [Formula: see text] and [Formula: see text], the concept of [Formula: see text]-distance Randić Estrada index of [Formula: see text] is studied. The notion of [Formula: see text]-distance Randić energy of [Formula: see text] is also investigated. Sharp lower and upper bounds for the [Formula: see text]-distance Randić Estrada index are obtained, and the extremal graphs are characterized. Additionally, a relation between the [Formula: see text]-distance Randić Estrada index and the [Formula: see text]-distance Randić energy of graphs is achieved. Moreover, a bound for the subdominant eigenvalues (eigenvalues different from the Perron value) of the [Formula: see text]-distance Randić matrix is presented.