On the minimum abc index of chemical trees

Author: ffie

August undefined, 2024

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. 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.

Computer search for trees with minimal ABC index - ScienceDirect

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 … 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 … gps wilhelmshaven personalabteilung

On structural properties of ABC-minimal chemical trees

Web6 de jun. de 2010 · The lower and upper bounds on ABC index of chemical trees in terms of the number of vertices were obtained in [3]. Also, it has been shown that the star K 1, n − 1, has the maximal ABC value of trees. 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 … Web15 de out. de 2024 · In this paper, we significantly refine the known features of the degree sequence of a tree with minimal ABC index. With the refined features a search program … gps wilhelmshaven

Maximum values of atom–bond connectivity index in the class …

On the minimum abc index of chemical trees

Experimental method for determining deformation in ABS and …

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. WebFor , if , then Corollary 10 implies that is the unique molecular tree with the minimum harmonic index; if , then Theorem 8 and Lemma 9 imply that is the unique molecular tree with the minimum harmonic index. If , then is not a molecular tree. The following gives the smallest value for with .. Theorem 11. Let and .Then the equality holds if and only if for …

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Web16 de jul. de 2009 · On the other hand, we strengthen a conjecture of Gutman et al. [Z. Naturforsch. 62a (2007), 495] that the Volkmann trees have maximal Estrada index among the trees with fixed maximum degree Δ, by conjecturing that the Volkmann trees also have maximal even spectral moments of any order. Web6 de abr. de 2024 · The atom-bond connectivity (ABC) index is a degree-based molecular descriptor that found diverse chemical applications. Characterizing trees with minimum ABC-index remained an elusive open problem even after serious attempts and is considered by some as one of the most intriguing open problems in mathematical …

http://www.sapub.org/global/showpaperpdf.aspx?doi=10.5923/j.am.20120241.02 Web2 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 physicochemical properties, the predictive power of GA index is somewhat better than predictive power of the Randić connectivity index.

Web19 de set. de 2014 · Furtula et al. [ 12 ], in the first serious mathematical works on ABC index obtained the chemical trees with extremal ABC values. They proved that, among all trees, the star tree, S_n, has the maximal ABC value. Web1 de nov. de 2013 · Given greedy trees perturbed by different degree sequences, we investigate the behaviors on their ABC index in this paper. Moreover, we also give the …

Web2 de abr. de 2024 · The ABC index of attains the maximum value if and only if both and are complete graphs. If the ABC index of attains the minimum value, then and must be trees. (2) Let and be trees. Then, the ABC index of attains the maximum value if and only if is a path and is a star. 1. Introduction

Web1 de dez. de 2024 · As applications, we determine the minimum ABC index and its structural properties of the chemical trees with n vertices and p pendant vertices in the case n ≥ 3 … gps will be named and shamedWeb1 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 gps west marineWeb1 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. gps winceWeb1 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 … gps weather mapWebThe fourth, the fifth and the sixth maximum chemical trees values of ABC−R for chemical trees, and the corresponding extremal graphs are determined, and an upper bound for ABC −R index of such trees with given number of pendant vertices is obtained. 1 PDF View 1 excerpt, references results gpswillyWeb9 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 … gps w farming simulator 22 link w opisieWeb1 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 … gps wilhelmshaven duales studium