the reciprocal degree distance (rdd)‎, ‎defined for a connected graph $g$ as vertex-degree-weighted sum of the reciprocal distances‎, ‎that is‎, ‎$rdd(g) =sumlimits_{u,vin v(g)}frac{d_g(u)‎ + ‎d_g(v)}{d_g(u,v)}.$ the reciprocal degree distance is a weight version of the harary index‎, ‎just as the degree distance is a weight version of the wiener index‎. ‎in this paper‎, ‎we present exact formu...

The Harary index is defined as the sum of reciprocals distances between all pairs vertices a connected graph G = (V, E). In this paper we introduce Index Power 3 Tree Mean graphs.

The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. A connected graph G is a cactus if any two of its cycles have at most one common vertex. Let G (n, r) be the set of cacti of order n and with r cycles, ξ(2n, r) the set of cacti of order 2n with a perfect matching and r cycles. In this paper, we give the sharp upper bounds of t...

In chemical graph theory, distance-degree-based topological indices are expressions of the form ∑ u6=v F (deg(u), deg(v)), d(u, v)), where F is a function, deg(u) the degree of u, and d(u, v) the distance between u and v. Setting F to be (deg(u) + deg(v))d(u, v), deg(u)deg(v)d(u, v), (deg(u)+deg(v))d(u, v)−1, and deg(u)deg(v)d(u, v)−1, we get the degree distance index DD, the Gutman index Gut, ...

In this paper, we present sharp bounds for the Zagreb indices, Harary index and hyperWiener index of graphs with a given matching number, and we also completely determine the extremal graphs. © 2010 Elsevier Ltd. All rights reserved.