The Randić index (R) and the geometric-arithmetic index (GA) are found to be useful tools in QSPR and QSAR studies. In the Journal of Inequalities and Applications 180, 1-7, Lokesha, Shwetha Shetty, Ranjini, Cangul, and Cevik gave "New bounds for Randić and GA indices." In the paper, we first point out that Theorems 1, 2, and 4 are incorrect and in this short note we present the correct inequalities for Randić and GA indices. In the same paper, we provide the equality cases for Theorems 3, 5, and 6.

The forgotten topological index is defined as the sum of cubes of the degrees of the vertices of the molecular graph G. In this paper, we obtain, analyze, and compare various lower bounds for the forgotten topological index involving the number of vertices, edges, and maximum and minimum vertex degree. Then we give Nordhaus-Gaddumtype inequalities for the forgotten topological index and coindex. Finally, we correct the number of extremal chemical trees on 15 vertices.

No abstract

The inverse degree of a graph G with no isolated vertices is defined as the sum of reciprocal of vertex degrees of the graph G. In this paper, we obtain several lower and upper bounds on inverse degree ID(G). Moreover, using computational results, we prove our upper bound is strong and has the smallest deviation from the inverse degree ID(G). Next, we compare inverse degree ID(G) with topological indices (Randić index R(G), geometric-arithmetic index GA(G)) for chemical trees and also we determine the n−vertex chemical trees with the minimum, the second and the third minimum, as well as the second and the third maximum of ID − R. In addition, we correct the second and third minimum Randić index chemical trees in [16].

The sum of reciprocals of distance between any two vertices in a graph G is called the Harary index. We determine the n-vertex extremal graphs with the maximum Harary index for all bipartite graphs, a given matching number, a given vertex-connectivity, and with a given edge-connectivity, respectively.