trees with extreme values of second zagreb index and coindex

The second zagreb index m2 (g) is equal to the sum of the products of the degrees of pairs of adjacent vertices and the second zagreb coindex m2 (g) is equal to the sum of the products of the degrees of pairs of non-adjacent vertices. kovijanić vukićević and popivoda (iranian j. math. chem. (2014) 19–29) prove that for any chemical tree of order n ≥ 5, m2 (t ) ≤ 8n − 26 n ≡ 0, 1 (mod 3) 8n − 24 otherwise. in this paper we present a generalization of the aforementioned bound for all trees in terms of the order and maximum degree. we also give a lower bound on the second zagreb coindex of trees.