On the minimum abc index of chemical trees

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August undefined, 2024

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 … 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 …

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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 … 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 … the origin of all fiber arts is

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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. 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. 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 the origin of airsoft

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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. 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 … the origin of a land floraWeb1 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 … the origin of a myth is usually unknown

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On the minimum abc index of chemical trees

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 … 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) …

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WebThe 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 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 …

Web15 de nov. de 2024 · Experimental method for determining deformation in ABS and ABS-PC plastic when simulated by the method of layer-by-layer fusing and comparison thereof when altering printing conditions: AIP Conference Proceedings: Vol 2171, No 1 No Access Published Online: 15 November 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 …

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 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.

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.

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 … the origin of a nameWeb16 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. the origin of ancient writing ielts readingWeb1 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] … the origin of american cultureWeb6 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 … the origin of amazonWeb1 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 … the origin of an animal taleWeb1 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 the origin of american individualismWeb12 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. the origin of anger