On the minimum abc index of chemical trees

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August undefined, 2024

WebOn structural properties of ABC-minimal chemical trees Downloadable (with restrictions)! The atom-bond connectivity (ABC) index of a connected graph G is defined as … Web5 de jun. de 2024 · As an interesting problem, we propose to characterize the trees with the minimum value of this index, and, here, we have some structural properties of these trees. We conclude this paper with few conjectures for possible further work.

Atom–bond connectivity index of quasi-tree graphs SpringerLink

WebLemma 1. Let and be positive integers such that . If is a tree such that is minimum among all the trees of , then contains at most one pendent path of length greater than 1.. Proof. Suppose, contrarily, that and are two pendent paths in , where and (note that the vertices and may coincide). If , then , and we have a contradiction to the choice of . Lemma 1 … Web1 de jul. de 2004 · We report here the results of the search for pairs of equienergetic acyclic molecular graphs (chemical trees) with the same number n of vertices. There are very … open rails msts routes

Atom-bond connectivity index of graphs - ScienceDirect

Web1 de dez. de 2024 · Given greedy trees perturbed by different degree sequences, we investigate the behaviors on their ABC index in this paper. Moreover, we also give the … WebThere are several vertex distance-based and degree-based indices which are introduced to analyze the chemical properties of molecule graph, for instance, Wiener index, PI index, Szeged index, and atom-bond connectivity index. Web13 de abr. de 2010 · Inspired by recent work on the atom-bond connectivity (ABC) index we propose here a new topological index, augmented Zagreb index (AZI). The tight upper … open rails cmk timetable

On structural properties of ABC-minimal chemical trees

Computation of M-Polynomial and Topological Indices of Phenol …

Web1 de fev. de 2012 · In fact, this is true for chemical trees with n≤6. n=2 This is the only possible arrangement for a chemical tree with 2 vertices. n=3 The chain is once again the only option. n=4 n=5 n=6 Thus for n≤6, the chain has the minimal ABC index. 4.3. Boris … Web9 de jun. de 2024 · Chem. 76 (2016) 131-140] gave rise to a conjecture about the minimum possible ABC-index of trees with a fixed number of leaves. We show that this conjecture … ip adresse hp envy 6000Web1 de set. de 2024 · Minimal values of VDB topological indices of chemical trees Let φ be a VDB topological index induced by the numbers {φ ( i, j )} (i,j) ∈ K and defined as (1). Since we are only interested in chemical trees, we may assume that K = { ( i, j) ∈ N × N: 1 ≤ i … ip adresse hostname

"Web1 de ago. de 2014 · The atom-bond connectivity (ABC) index of a connected graph Gis defined as ABC(G)=∑uv∈E(G)d(u)+d(v)−2d(u)d(v),where d(w) is the degree of vertex win Gand E(G) is the set of edges of G. Given greedy trees perturbed by different degree sequences, we investigate the behaviors on their ABC index in this paper. " - On the minimum abc index of chemical trees

On the minimum abc index of chemical trees

[1804.02098] The evolution of the structure of ABC-minimal trees

Web7 de jan. de 2014 · The cardinalities of V ( G) and E ( G) are called the order and size of G, respectively. The atom-bond connectivity index ( ABC index for short) of G is defined as \begin {aligned} ABC (G) = \sum_ {uv\in E (G)} \sqrt {\frac {d (u)+d (v)-2} {d (u)d (v)}}, \end {aligned} where d ( u) is degree of the vertex u.

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Web1 de fev. de 2012 · A complete characterization of trees with minimal $ABC$ index is still an open problem. In this paper, we present new structural properties of trees with … WebThe paper outlines the results known for W of trees: methods for computation of W and combinatorial expressions for W for various classes of trees, the isomorphism–discriminating power of W, connections between W and the center and centroid of a tree, as well as between W and the Laplacian eigenvalues, results on the …

Web1 de out. de 2012 · The ABC index is a degree-based molecular structure descriptor, that found chemical applications. Finding the connected graph(s) of a given order whose ABC … Web1 de dez. de 2024 · Although we deal with the case of the chemical trees with n vertices and p pendant vertices for n ≥ 3 p − 2, these new methods are significative attempt in …

Web1 de out. de 2012 · Our algorithm for identifying the minimum-ABC tree(s) consists of two successive steps: (1) Generating the trees using a recursive scheme. (2) Computing the … Web1 de dez. de 2024 · In this paper, we present an efficient approach of computing trees with minimal ABC index, by considering the degree sequences of trees and some known …

Web4 de fev. de 2024 · Abstract. For a graph , its sum-connectivity index is denoted by and is defined as the sum of the numbers over all edges of , where denotes the degree of a vertex . In this study, we find a sharp lower bound on the sum-connectivity index of graphs having minimum degree of at least 3 under certain constraints and characterize the …

Web13 de abr. de 2010 · Abstract Inspired by recent work on the atom-bond connectivity ( ABC) index we propose here a new topological index, augmented Zagreb index ( AZI ). The tight upper and lower bounds for chemical trees are obtained. Moreover, it has been shown that among all trees the star has the minimum AZI value. ip adresse magenta routerWeb1 de mai. de 2024 · The atom-bond connectivity ( ABC) index provides a good model for the stability of linear and branched alkanes as well as the strain energy of cycloalkanes. For certain physico-chemical properties, the predictive power of GA index is somewhat better than predictive power of the Randić connectivity index. In this paper, we have studied the open rails indian railway pc downloadWeb1 de mar. de 2000 · As far as we know, the mathematical properties of related indices for molecular trees have been studied extensively. For example, Gutman et al. [13, 14] … openrailwaymap奥维Web12 de set. de 2024 · The ABC index plays a key role in correlating the physical–chemical properties and the molecular structures of some families of compounds. In this paper, we … openrailway wifiWeb1 de jan. de 2012 · On the Minimum ABC Index of Chemical Trees Authors: Tzvetalin S. Vassilev Nipissing University Laura J. Huntington Abstract The Atom Bond Connectivity … ip adresse in bitWebOn structural properties of ABC-minimal chemical trees Downloadable (with restrictions)! The atom-bond connectivity (ABC) index of a connected graph G is defined as ABC(G)=∑uv∈E(G)d(u)+d(v)−2d(u)d(v), where d(w) is the degree of vertex w in G and E(G) is the set of edges of G. openrailway projectWeb1 de fev. de 2012 · implications to the minimum/maximum ABC index on graphs. With relation to trees, it is known that among all the trees of the same number of vertices, the … ip adresse in windows 10 ändern