Chemical structures of organic compounds are characterized numerically by a variety of structural descriptors, one of the earliest and most widely used being the Wiener index W, derived from the interatomic distances in a molecular graph. Extensive use of such structural descriptors or topological indices has been made in drug design, screening of chemical databases, and similarity and diversit...

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.

Let G = (V,E), V {v1, v2,..., vn}, be a simple connected graph of order n and size m, with vertex degree sequence d1 ? d2 ...? dn. A is said to regular if =... Otherwise it irregular. In many applications problems important know how irregular given is. quantity called deviation S(G) ?ni=1 |di-2m/n| can used as an irregularity measure. Some new lower bounds for are obtained. formula computing bi...

The energy of a graph G is equal to the sum of absolute values of the eigenvalues of the adjacency matrix of G, whereas the Laplacian energy of a graph G is equal to the sum of the absolute value of the difference between the eigenvalues of the Laplacian matrix of G and the average degree of the vertices of G. Motivated by the work from Sharafdini an...

Mathematical descriptors of molecular structure, such as various topological indices, have been widely used in structure-property-activity studies (see [5, 6, 12]). Among the numerous topological indices considered in chemical graph theory, only a few have been found noteworthy in practical application (see [10]). One of these is the connectivity index or Randić index. The Randić index of an or...

Let G= V E be a simple connected graph. The distance between two vertices of G is defined to be the length of the shortest path between the two vertices. There are topological indices assigned to G and based on the distance function which are invariant under the action of the automorphism group of G. Some important indices assigned to G are the Wiener, Szeged, and PI index which we will find th...

Graph Based Characterization of Distributed Applications Markus Braun, Gabriele Kotsis Institute of Applied Computer Science and Information Systems University of Vienna Lenaugasse 2/8, A-1080 Wien,  Osterreich [braunjgabi]@ani.univie.ac.at Abstract| Timed Structural Parallelism Graph (TSPG) have been proposed as a graph model representing the coarse grain dependency and communication structur...

For a (molecular) graph, the multiplicative Zagreb indices ∏ 1-index and ∏ 2index are multiplicative versions of the ordinary Zagreb indices (M1-index and M2index). In this note we report several sharp upper bounds for ∏ 1-index in terms of graph parameters including the order, size, radius, Wiener index and eccentric distance sum, and upper bounds for ∏ 2-index in terms of graph parameters inc...