General sum-connectivity index and general Randic index of trees with given maximum degree

Abstract

For trees with given number of vertices n and maximum degree ∆ , we present lower bounds on the general sum-connectivity index χ a if a > 0 and 3 ≤ ∆ ≤ n − 1 , and an upper bound on the general Randi´c index R a if − 0 . 283 ≤ a < 0 and 3 ≤ ∆ ≤ (cid:98) n − 1 2 (cid:99) . All the extremal trees for our bounds are given.