Covering a convex body by its homothets is a classical notion in discrete geometry that has resulted in a number of interesting and long-standing problems. Swanepoel introduced the covering parameter of a convex body as a means of quantifying its covering properties. In this paper, we introduce two relatives of the covering parameter called covering index and weak covering index, which upper bo...

A lot of research and various techniques have been devoted for finding the topological descriptor Wiener index, but most of them deal with only particular cases. There exist three regular plane tessellations, composed of the same kind of regular polygons namely triangular, square, and hexagonal. Using edge congestion-sum problem, we devise a method to compute the Wiener index and demonstrate th...

The adjacent eccentric distance sum index of a graph G is defined as ξsv(G) = ∑ v∈V (G) ε(v)D(v) deg(v) , where ε(v), deg(v) denote the eccentricity, the degree of the vertex v, respectively, and D(v) = ∑ u∈V (G) d(u, v) is the sum of all distances from the vertex v. In this paper we derive some upper or lower bounds for the adjacent eccentric distance sum in terms of some graph invariants or t...

QSAR study has been carried out on the MMP-13 inhibitory activity of fused pyrimidine derivatives possessing a1,2,4-triazol-3-yl group as a ZBG in 0D- to 2D-Dragon descriptors. The derived models have revealed that number Sulfur atoms (descriptor nS), Balaban mean square distance index MSD), molecular electrotopological variation DELS), structural information content neighborhood symmetry 2nd a...

A Poincaré-Hopf theorem in the spirit of Pugh is proven for compact orbifolds with boundary. The theorem relates the index sum of a smooth vector field in generic contact with the boundary orbifold to the EulerSatake characteristic of the orbifold and a boundary term. The boundary term is expressed as a sum of Euler characteristics of tangency and exitregion orbifolds. As a corollary, we expres...

Covering a convex body by its homothets is a classical notion in discrete geometry that has resulted in a number of interesting and long-standing problems. Swanepoel [Mathematika 52 (2005), 47–52] introduced the covering parameter of a convex body as a means of quantifying its covering properties. In this paper, we introduce a relative of the covering parameter called covering index, which turn...

Chemical structures of organic compounds are characterized numerically by a variety of structural descriptors computed either from the molecular graph or from the three-dimensional (3D) molecular geometry. Extensive use of such structural descriptors or topological indices has been made in drug design, screening of chemical databases, similarity and diversity assessment, and quantitative struct...

The Wiener index of a graph Gis defined as W(G) =1/2[Sum(d(i,j)] over all pair of elements of V(G), where V (G) is the set of vertices of G and d(i, j) is the distance between vertices i and j. In this paper, we give an algorithm by GAP program that can be compute the Wiener index for any graph also we compute the Wiener index of HAC5C7[p, q] and HAC5C6C7[p, q] nanotubes by this program.

For a graph, the first Zagreb index M1 is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M2 is equal to the sum of the products of the degrees of pairs of adjacent vertices. Denote by Gn,k the set of graphs with n vertices and k cut edges. In this paper, we showed the types of graphs with the largest and the second largest M1 and M2 among Gn,k .