Mobeen Munir 1, Waqas Nazeer 1, Shazia Rafique 2 and Shin Min Kang 3,4,* 1 Division of Science and Technology, University of Education, Lahore 54000, Pakistan; [email protected] (M.M.); [email protected] (W.N.) 2 Center for Excellence in Molecular Biology, Punjab University Lahore, Lahore 53700, Pakistan; [email protected] 3 Department of Mathematics and Research Institute of Natural ...

General formulas are obtained for the vertex Padmakar-Ivan index (PIv) of tetrathiafulvalene (TTF) dendrimer, whereby TTF units we are employed as branching centers. The PIv index is a Wiener-Szeged-like index developed very recently. This topological index is defined as the summation of all sums of nu(e) and nv(e), over all edges of connected graph G.

We derive sharp lower bounds for the first and the second Zagreb indices (M1 and M2 respectively) for trees and chemical trees with the given number of pendent vertices and find optimal trees. M1 is minimized by a tree with all internal vertices having degree 4, while M2 is minimized by a tree where each “stem” vertex is incident to 3 or 4 pendent vertices and one internal vertex, while the res...

Several different topological indices (the carbon number, the Wiener index, the Balaban dis­ tance sum connectivity index, the Randic molecular identification number, and the Randic molecular connectivity indices °/, 2%, 3̂ p and 3/ c) were employed in the correlation of the velocity of ultrasonic sound in a variety of alkane and alcohol species. Using linear regression analyses and published so...

The first reformulated Zagreb index $EM_1(G)$ of a simple graph $G$ is defined as the sum of the terms $(d_u+d_v-2)^2$ over all edges $uv$ of $G .$ In this paper, the various upper and lower bounds for the first reformulated Zagreb index of a connected graph interms of other topological indices are obtained.

We give conditions on the numbers {φij} under which a vertexdegree-based topological index TI of the form

Let G be a graph and let mij(G), i, j ≥ 1, be the number of edges uv of G such that {dv(G), du(G)} = {i, j}. TheM -polynomial ofG is introduced withM(G;x, y) = ∑ i≤j mij(G)x y . It is shown that degree-based topological indices can be routinely computed from the polynomial, thus reducing the problem of their determination in each particular case to the single problem of determining the M -polyn...

The current work introduces an algorithm for constructing Reeb graph for CAD models and their inner cavities. The nodes of the graph represent areas of the manifold of the model where topological changes occur. Edges of the graph encode information about connections between such areas. The outline for the topological graph matching is given for detection of graph (sub)isomorphism. The proposed ...

topological indices are one of the oldest and most widely used descriptors in quantitative structureproperties relationvhips (qspr). amongst the topological indices used a,s descriptors in qspic., the wienerindex is by far the most popular index. as it has been shown that the wiener index has a strong correlationwith the chemical propenies of the compound.in this study, the relationship between...