We consider four classes of graphs arising from a given graph via different types of edge subdivisions. We present explicit formulas expressing their eccentric connectivity index in terms of the eccentric connectivity index of the original graph and some auxiliary invariants.

In the visual cortex of the monkey the horizontal organization of the preferred orientations of orientation-selective cells follows two opposing rules: 1) neighbors tend to have similar orientation preferences, and 2) many different orientations are observed in a local region. Several orientation models which satisfy these constraints are found to differ in the spacing and the topological index...

Mobeen Munir 1, Waqas Nazeer 1, Abdul Rauf Nizami 1, Shazia Rafique 2 and Shin Min Kang 3,4,* 1 Division of Science and Technology, University of Education, Lahore 54000, Pakistan; mmunir@ue.edu.pk (M.M.); nazeer.waqas@ue.edu.pk (W.N.); arnizami@ue.edu.pk (A.R.N.) 2 Center for Excellence in Molecular Biology, Punjab University Lahore, Lahore 53700, Pakistan; shaziarafique@gmail.com 3 Department...

In this note, we derive the lower bound on the sum for Wiener index of bipartite graph and its bipartite complement, as well as the lower and upper bounds on this sum for the Randić index and Zagreb indices. We also discuss the quality of these bounds.

By the generalization of Chern–Simons topological current and Gauss–BonnetChern theorem, the purpose of this paper is to make a non-Abelian gauge field theory foundation of the topological current of p̃-branes formulated in our previous work. Using φ–mapping topological current theory proposed by Professor Duan, we find that the topological p̃-branes are created at every isolated zero of vector f...

In this paper we study lower bounds in a unified way for large family of topological indices, including the first variable Zagreb index M 1 ? . Our aim is to obtain sharp inequalities and characterize corresponding extremal graphs. The main results provide several vertex-degree-based indices. These are new even Zagreb, inverse forgotten

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...

In chemical graph theory, distance-degree-based topological indices are expressions of the form ∑ u6=v F (deg(u), deg(v)), d(u, v)), where F is a function, deg(u) the degree of u, and d(u, v) the distance between u and v. Setting F to be (deg(u) + deg(v))d(u, v), deg(u)deg(v)d(u, v), (deg(u)+deg(v))d(u, v)−1, and deg(u)deg(v)d(u, v)−1, we get the degree distance index DD, the Gutman index Gut, ...

The strong chromatic index of a graph G, denoted by s ′ (G), is the minimum number of colors in a coloring of edges of G such that each color class is an induced matching. Erdős and Nešetřil conjectured that s ′ (G) ≤ 5 4 ∆ 2 for all graphs G with maximum degree ∆. The problem is far from being solved and the best known upper bound on s ′ (G) is 1.99∆ 2. We will discuss the topological variant ...

Phenol formaldehyde (phenolic resin) has a wide range of moldings. However, it immense consumption in manufacturing electrical equipment due to its insulating property. Phenolic resin retains properties at the freezing point, and also age cannot be determined. Due insulator property, use equipment. In this article, degree-based topological indices phenol are determined with help M-polynomial. W...