Abstract In this paper, we give various lower and upper bounds for the energy of graphs in terms several topological indices graphs: first general multiplicative Zagreb index, Randić zeroth-order redefined indices, atom-bond connectivity index. Moreover, obtain new certain graph invariants as diameter, girth, algebraic radius.

If $G$ is a connected graph with vertex set $V$, then the eccentric connectivity index of $G$, $xi^c(G)$, is defined as $sum_{vin V(G)}deg(v)ecc(v)$ where $deg(v)$ is the degree of a vertex $v$ and $ecc(v)$ is its eccentricity. In this paper we show some convergence in probability and an asymptotic normality based on this index in random bucket recursive trees.

The Wiener index of a graph is defined as the sum of distances between all pairs of vertices in a connected graph. Wiener index correlates well with many physio chemical properties of organic compounds and as such has been well studied over the last quarter of a century. In this paper we prove some general results on Wiener Index for graphs using degree sequence.

The stress of a vertex is node centrality index, which has been introduced by Shimbel (1953). in graph the number geodesics (shortest paths) passing through it. In this paper, we introduce new topological index for graphs called square root sum using stresses vertices. Further, establish some inequalities, prove results and compute stress-sum standard graphs.

This lecture introduces a generalization of Nash equilibrium due to Aumann [1] known as correlated equilibrium, which allows for possible dependencies in strategic choices. A daily example of a correlated equilibrium is a traffic light: a red (green) signal suggests that cars should stop (go), and following each suggestion is of course rational. Following Aumann [2], we present two definitions ...

The general Randić index of an organic molecule whose molecular graph is G is defined as the sum of (d(u)d(v))α over all pairs of adjacent vertices of G, where d(u) is the degree of the vertex u in G and α is a real number with α 6= 0. In the paper, we obtained sharp bounds on the general Randić index of the Nordhaus-Gaddum type for trees. Also we show that the general Randić index of the Nordh...