On the minimum abc index of chemical trees

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August undefined, 2024

Web1 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 … 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 …

Experimental method for determining deformation in ABS and …

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 … hayward justin

On structural properties of ABC-minimal chemical trees

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 describe the structural properties of graphs which have the minimum ABC index among all connected graphs with a given degree sequence. 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 … 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 … boucherie tedos

A Note on the Minimum Wiener Polarity Index of Trees with a …

Molecules with smallest connectivity indices Request PDF

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 … 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 boucherie tavers le boeuf tricoloreWebThere 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. hayward key assembly replacement

"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 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. " - On the minimum abc index of chemical trees

On the minimum abc index of chemical trees

Efficient computation of trees with minimal atom-bond …

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 … 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 …

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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. 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 … 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 …

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 … 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.

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 … boucherie tassoul rhisnes horairesWeb13 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 … boucherie teddy moncheauxWebIn 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 … boucherie tayeb istresWeb7 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. hayward key coverWeb1 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 boucherie tarallhttp://www.sapub.org/global/showpaperpdf.aspx?doi=10.5923/j.am.20120241.02 hayward knife sharpeningWeb1 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 … boucherie teddy