We describe a new algorithm for calculating the topological degree deg (f, B, 0) where B ⊆ Rn is a product of closed real intervals and f : B → Rn is a real-valued continuous function given in the form of arithmetical expressions. The algorithm cleanly separates numerical from combinatorial computation. Based on this, the numerical part provably computes only the information that is strictly ne...

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 ...

The concept of Sombor index (SO) was recently introduced by Gutman in the chemical graph theory. It is a vertex-degree-based topological and denoted SO: SO=SO(G)=?vivj?E(G)dG(vi)2+dG(vj)2, where dG(vi) degree vertex vi G. Here, we present novel lower upper bounds on graphs using some parameters. Moreover, obtain several relations with first second Zagreb indices graphs. Finally, give conclusion...

the present note is devoted to establish some extremal results for the zeroth-order general randi'{c} index of cacti, characterize the extremal polyomino chains with respect to the aforementioned index, and hence to generalize two already reported results.

let g be a graph. in this paper, we study the eccentric connectivity index, the new version ofthe second zagreb index and the forth geometric–arithmetic index.. the basic properties ofthese novel graph descriptors and some inequalities for them are established.

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 isa wiener-szeged-like index developed very recently. this topological index is defined as thesummation of all sums of nu(e) and nv(e), over all edges of connected graph g.

1. In previous papers [2; 3], the problem of proving an existence theorem for a certain functional equation was reduced to that of computing the topological degree of a mapping in Euclidean w-space defined by homogeneous polynomials or infinite series. The complex case of the latter problem was solved in [4]. Since the problem is analogous to that of studying the roots of a polynomial equation,...

Objective: Metal concentrations in 53 soil samples of Shahr-e-Babak were determined.  Methods: Assessment of enrichment factor and geo-accumulation index revealed higher degree of contamination of Cd, Pb, and Cu in soil samples. Moreover, results of metal fractionation study revealed high amount of Cd and Pb are associated in weakly bounds may lead to environmental risk of these metals.  Result...