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Kiran Naz;Sarfraz Ahmad;Hafiz Muhammad Bilal;Muhammad Kamran Siddiqui; 《International journal of quantum chemistry》2024,124(12):e27435
A polymer is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. The bulky and normal polymers are graphs of aromatic organic compounds. The main idea of this article is to elaborate the expected results of Zagreb connection, sombor and reduced sombor indices in bulky and normal polymers. The generalized expected results with the help of probability technique for all the chains like polyonino, pentachain, polyphenyl, cyclooctane cyclodecane and so on different chains for Alkanes have been determined which are connected with and without any bond (edge). The Sombor topological index is named after the city of Sombor in Serbia, where it was introduced by a group of researchers in the field of chemoinformatics and mathematical chemistry. At the end, we have find the meta, ortho and para polymers to define the average values of Zagreb connection, Sombor and reduced Sombor indices. 相似文献
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For a non-zero real number α, let s α (G) denote the sum of the αth power of the non-zero Laplacian eigenvalues of a graph G. In this paper, we establish a connection between s α (G) and the first Zagreb index in which the Hölder’s inequality plays a key role. By using this result, we present a lot of bounds of s α (G) for a connected (molecular) graph G in terms of its number of vertices (atoms) and edges (bonds). We also present other two bounds for s α (G) in terms of connectivity and chromatic number respectively, which generalize those results of Zhou and Trinajsti? for the Kirchhoff index [B Zhou, N Trinajsti?. A note on Kirchhoff index, Chem. Phys. Lett., 2008, 455: 120–123]. 相似文献
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It was conjectured that for each simple graph G=(V,E) with n=|V(G)| vertices and m=|E(G)| edges, it holds M2(G)/m≥M1(G)/n, where M1 and M2 are the first and second Zagreb indices. Hansen and Vuki?evi? proved that it is true for all chemical graphs and does not hold in general. Also the conjecture was proved for all trees, unicyclic graphs, and all bicyclic graphs except one class. In this paper, we show that for every positive integer k, there exists a connected graph such that m−n=k and the conjecture does not hold. Moreover, by introducing some transformations, we show that M2/(m−1)>M1/n for all bicyclic graphs and it does not hold for general graphs. Using these transformations we give new and shorter proofs of some known results. 相似文献
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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
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Z.B. Maksić K. Rupnik M. Eckert-Maksić 《Journal of Electron Spectroscopy and Related Phenomena》1979,16(3):371-377
The keto—enol tautomerism in malonaldehyde and some related 1,3-diketones is thoroughly discussed by the calculation of inner-core binding energies. The semiempirical wave-functions were obtained by the self-consistent charge (SCC—MO) molecular orbital procedure. The calculated O(1s) binding energies are generally in good agreement with available experimental data. The discrepancy found for the alcohol-type oxygen in acetylacetone is so large that it strongly indicates an error in experimental assignment. The calculations also provide conclusive evidence that enol-forms possess asymmetric hydrogen-bonded protons. 相似文献
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Resolution enhancement of a.c. polarographic peaks by deconvolution using the fast fourier transform
A method for resolution enhancement of a.c. polarograms (voltammograms) is presented. The method is based on deconvolution using fast Fourier transforms. Overlapped a.c. polarograms are mathematically narrowed and sharpened, retaining the peak position and linear proportionality of the sharpened peak height with concentration. The advantages and limitations of the method are demonstrated on simulated and experimental a.c. polarograms. The same approach is applicable to related techniques such as. differential pulse and square-wave polarography. 相似文献
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We examine the quantity over sets of graphs with a fixed number of edges. The main result shows the maximum possible value of is achieved by three different classes of constructions, depending on the distance between the number of edges and the nearest triangular number. Furthermore we determine the maximum possible value when the set of graphs is restricted to be bipartite, a forest, or to be planar given sufficiently many edges. The quantity corresponds to the difference between two well studied indices, the irregularity of a graph and the sum of the squares of the degrees in a graph. These are known as the first and third Zagreb indices in the area of mathematical chemistry. 相似文献