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1.
The first Zagreb index M 1(G) is equal to the sum of squares of the degrees of the vertices, and the second Zagreb index M 2(G) is equal to the sum of the products of the degrees of pairs of adjacent vertices of the underlying molecular graph G. In this paper we obtain an upper bound on the first Zagreb index M 1(G) of G in terms of the number of vertices (n), number of edges (m), maximum vertex degree (Δ1), second maximum vertex degree (Δ2) and minimum vertex degree (δ). Using this result we find an upper bound on M 2(G). Moreover, we present upper bounds on and in terms of nm, Δ1, Δ2, δ, where denotes the complement of G.  相似文献   

2.
Sharp Bounds for the Second Zagreb Index of Unicyclic Graphs   总被引:1,自引:0,他引:1  
The second Zagreb index M 2(G) of a (molecule) graph G is the sum of the weights d(u)d(v) of all edges uv of G, where d(u) denotes the degree of the vertex u. In this paper, we give sharp upper and lower bounds on the second Zagreb index of unicyclic graphs with n vertices and k pendant vertices. From which, and C n have the maximum and minimum the second Zagreb index among all unicyclic graphs with n vertices, respectively.  相似文献   

3.
Among the 16 expressions derived in the recent paper [Int. J. Quantum Chem. 2020 , 120(6), e26082] for calculating certain degree-based topological indices of the molecular graphs of carbon nanocones and nanotori, 12 expressions contain some mistakes, and the remaining 4 follow from an already existing general expression. In this note, the correct versions of the aforementioned erroneous expressions are obtained.  相似文献   

4.
5.
We find a necessary and sufficient conditions on a sequence
for the existence of an acyclic molecular graph G such that exactly m ij edges connect vertices of degree i and j. We use this result together with two additional results to make an algorithm that generates all the sequences
such that a molecular acyclic graph exists with exactly m ij edges connecting vertices of degree i and j. This algorithm is utilized to compare discriminative properties of the Zagreb index and the modified Zagreb index, and it is found that the modified Zagreb index is more discriminative then the Zagreb index.  相似文献   

6.
A new extension of the generalized topological indices (GTI) approach is carried out to represent “simple” and “composite” topological indices (TIs) in an unified way. This approach defines a GTI-space from which both simple and composite TIs represent particular subspaces. Accordingly, simple TIs such as Wiener, Balaban, Zagreb, Harary and Randić connectivity indices are expressed by means of the same GTI representation introduced for composite TIs such as hyper-Wiener, molecular topological index (MTI), Gutman index and reverse MTI. Using GTI-space approach we easily identify mathematical relations between some composite and simple indices, such as the relationship between hyper-Wiener and Wiener index and the relation between MTI and first Zagreb index. The relation of the GTI-space with the sub-structural cluster expansion of property/activity is also analysed and some routes for the applications of this approach to QSPR/QSAR are also given.  相似文献   

7.
Let G = (V, E) be a simple connected graph with vertex set V and edge set E. The Wiener index W(G) of G is the sum of distances between all pairs of vertices in G, i.e., , where d G (u, v) is the distance between vertices u and v in G. In this paper, we first give a new formula for calculating the Wiener index of an (n,n)-graph according its structure, and then characterize the (n,n)-graphs with the first three smallest and largest Wiener indices by this formula.  相似文献   

8.
A new method proposed for solving QSPR tasks is based on transition from numerical values to topological equivalents (TEs) of physicochemical properties of chemical compounds. The TEs are unambiguously related to corresponding properties; for n-alkanes, they are linear functions of the number, n, of carbon atoms. Since the TE depends only on the corresponding physicochemical parameter, it can be calculated for any hydrocarbon using the same relationships as those known for n-alkanes. The optimal topological index (OTI) constructed using the chemical structure matrix for TEs usually has a much smaller basis compared to the topological index obtained by analogous procedure for the physicochemical property. An algorithm for modeling of physicochemical properties using the TEs was developed and evaluated taking the octane numbers of alkanes and cycloalkanes as examples. Dedicated to Academician G. A. Abakumov on the occasion of his 70th birthday. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1619–1631, September, 2007.  相似文献   

9.
10.
The chromatographic hydrophobicity index (CHI) is an HPLC‐based parameter that provides reliable guidance in optimization of pharmacological efficiency and adsorption, distribution, metabolism and exertion (ADME) profile of drug candidates. In the present work, classical and three‐dimensional quantitative structure–property relationship (QSPR) models were developed for prediction of CHI values of some 4‐hydroxycoumarin analogs on immobilized artificial membrane column. Comparative molecular field analysis (CoMFA) and comparative molecular similarity indices analysis (CoMSIA) as 3D–QSPR methods were performed to gain insight into the key structural factors affecting on the chromatographic hydrophobicity of interested chemicals. The calculated parameters of Q 2, R 2 and standard error were 0.545, 0.996 and 0.773 for CoMFA model and 0.815, 0.986 and 1.44 for CoMSIA model, respectively. The contour maps for steric fields of the CoMFA model illustrate that the hydrophobicity of chemicals will be higher when the positions of R6, R7 and R8 in the 4‐hydroxycuomarin ring are substituted by alkyl groups. Moreover, by the analysis of the plots of electrostatic fields, it was concluded that the CHI value greatly increases if one hydrogen on coumarin ring is substituted by the F, Cl, Br, OH or OCH3 group.  相似文献   

11.
Entropy is a thermodynamic function in chemistry that reflects the randomness and disorder of molecules in a particular system or process based on the number of alternative configurations accessible to them. Distance-based entropy is used to solve a variety of difficulties in biology, chemical graph theory, organic and inorganic chemistry, and other fields. In this article, the characterization of the crystal structure of niobium oxide and a metal–organic framework is investigated. We also use the information function to compute entropies by building these structures with degree-based indices including the K-Banhatti indices, the first redefined Zagreb index, the second redefined Zagreb index, the third redefined Zagreb index, and the atom-bond sum connectivity index.  相似文献   

12.
In theoretical chemistry the quantitative parameters which are used to describe the atomic topology of graphs are termed as topological indices. Through these topological indices many physical and chemical characteristics such as melting point, entropy, energy generation and vaporisation enthalpy of chemical compounds can be predicted. The theory of graphs has a significant use in measuring the relationship of certain associated graphs with various topological indices. In this paper, we compute novel topological indices based on eV- and ve-degrees for starphene St[n,m,l] and fenestrene F[n,m]. A Maple-based algorithm is proposed for the calculation of ve and eV-degree based topological indices from the graph adjacency matrix.  相似文献   

13.
We report some properties of the reciprocal molecular topological index RMTI of a connected graph, and, in particular, its relationship with the first Zagreb index M1. We also derive the upper bounds for RMTI in terms of the number of vertices and the number of edges for various classes of graphs, including K r+1 -free graphs with r ≥ 2, quadrangle-free graphs, and cacti. Additionally, we consider a Nordhaus-Gaddum-type result for RMTI.  相似文献   

14.
An efficient structure filtration method for the operation with chemical databases containing information on the structures and properties of organic molecules was proposed. The technique involves the use of electronegativity indices for generation of identification keys and for isomorphism tests of the molecular graphs corresponding to the structural formulas. The test set for the method proposed included a total of 95,000,000 molecules containing up to sixty carbon atoms. Tests revealed a high discriminating capability of the electronegativity indices and high efficiency of the method for solving both general problems (recognition of chemical structures, chemical database management systems) and specific tasks (generation of molecular graphs, etc.) in chemical informatics. Dedicated to Academician N. S. Zefirov on the occasion of his 70th birthday. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 2166–2176, September, 2005.  相似文献   

15.
杨翌秋  许禄 《应用化学》1993,10(6):49-52
本文提出一种新的拓扑指数-EA系列指数,它是从表示分子图形的邻接矩阵出发,结合图形中顶点的度构造成EA矩阵,计算EA矩阵的本征值,求出本征值绝对值和指数EAΣ及本征值绝对值最大值指数EAmax,实验表明,EA系列指数具有良好的唯一性和相关性。  相似文献   

16.
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18.
Optimal topological indices for particular physicochemical properties can be designed using the chemical structure matrix. Taking the alkane boiling points as examples, the extrapolation properties of some well-known topological indices were compared with those of the optimal topological indices designed ad hoc. The advantages of the new indices are shown. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1454–1461, September, 2006.  相似文献   

19.
20.
The notion of the chemical structure matrix (CSM) is introduced. The columns of the CSM represent the numbers of occurrences of different subgraphs in molecular graphs and are treated as vectors in a linear space. Any topological indices and physicochemical properties can also be treated as vectors in the same linear space. The QSPR problem is formally reduced to the search for linear correlations between vectors. A simple procedure for solving the problem is proposed. A novel method for establishing QSAR is outlined. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1447–1453, September, 2006.  相似文献   

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