Distance-based indices of complete m-ary trees

Abstract

Binary and [Formula: see text]-ary trees have extensive applications, particularly in computer science and chemistry. We present exact values of all important distance-based indices for complete [Formula: see text]-ary trees. We solve recurrence relations to obtain the value of the most well-known index called the Wiener index. New methods are used to express the other indices (the degree distance, the eccentric distance sum, the Gutman index, the edge-Wiener index, the hyper-Wiener index and the edge-hyper-Wiener index) as well. Values of distance-based indices for complete binary trees are corollaries of the main results.