On the minimum abc index of chemical trees

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 … 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.

On the Graphs of Minimum Degree At Least 3 Having Minimum …

Web6 de abr. de 2024 · 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 … 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 … sharon bill grade 2 theory https://foxhillbaby.com

Augmented Zagreb index SpringerLink

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 … 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 … 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. sharonbill.com

Efficient computation of trees with minimal atom-bond …

Category:Wiener Index of Trees: Theory and Applications SpringerLink

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On the minimum abc index of chemical trees

On structural properties of ABC -minimal chemical trees

Web9 de jun. de 2024 · The atom-bond connectivity (ABC) index is a degree-based molecular descriptor with diverse chemical applications. Recent work of Lin et al. [W. Lin, J. Chen, C. Ma, Y. Zhang, J. Chen, D. Zhang, and F. Jia, On trees with minimal ABC index among trees with given number of leaves, MATCH Commun. Math. Comput. Chem. 76 (2016) … 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 …

On the minimum abc index of chemical trees

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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 … http://www.sapub.org/global/showpaperpdf.aspx?doi=10.5923/j.am.20120241.02

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. 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 …

Web1 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 … WebIn this paper we further investigate the trees that minimize the ABC index. Our investigations are limited to chemical trees, i.e. trees in which the maximum vertex degree is 4. The …

Web25 de set. de 2024 · Let G be a simple, connected and undirected graph. The atom-bond connectivity index (ABC(G)) and Randić index (R(G)) are the two most well known topological indices. Recently, Ali and Du (2024) introduced the difference between atom-bond connectivity and Randić indices, denoted as ABC−R index. In this paper, …

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 … population of silt coWebOn 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. sharon bill music theory grade 1Web1 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 … sharon bill music theory grade 2sharon bilterman obituaryWebOn structural properties of ABC-minimal chemical trees Downloadable (with restrictions)! The atom-bond connectivity (ABC) index of a connected graph G is defined as … population of silsden west yorkshireWeb7 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. sharon billinsWeb1 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 … population of sikhs in india