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《Discrete Mathematics》2022,345(12):113083
Let G be a graph, the order of G, the connectivity of G and k a positive integer such that . Then G is said to be k-extendable if it has a matching of size k and every matching of size k extends to a perfect matching of G. A Hamiltonian path of a graph G is a spanning path of G. A bipartite graph G with vertex sets and is defined to be Hamiltonian-laceable if such that and for every pair of vertices and , there exists a Hamiltonian path in G with endpoints p and q, or and for every pair of vertices , there exists a Hamiltonian path in G with endpoints p and q. Let G be a bipartite graph with bipartition . Define to be a maximum integer such that and (1) for each non-empty subset S of X, if , then , and if , then ; and (2) for each non-empty subset S of Y, if , then , and if , then ; and (3) if there is no non-negative integer satisfying (1) and (2).Let G be a bipartite graph with bipartition such that and . In this paper, we show that if , then G is Hamiltonian-laceable; or if , then for every pair of vertices and , there is an -path P in G with . We show some of its corollaries in k-extendable, bipartite graphs and a conjecture in k-extendable graphs. 相似文献
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Yandong Guo 《中国物理 B》2022,31(12):127201-127201
Controlling the spin transport at the single-molecule level, especially without the use of ferromagnetic contacts, becomes a focus of research in spintronics. Inspired by the progress on atomic-level molecular synthesis, through first-principles calculations, we investigate the spin-dependent electronic transport of graphene nanoflakes with side-bonded functional groups, contacted by atomic carbon chain electrodes. It is found that, by rotating the functional group, the spin polarization of the transmission at the Fermi level could be switched between completely polarized and unpolarized states. Moreover, the transition between spin-up and spin-down polarized states can also be achieved, operating as a dual-spin filter. Further analysis shows that, it is the spin-dependent shift of density of states, caused by the rotation, that triggers the shift of transmission peaks, and then results in the variation of spin polarization. Such a feature is found to be robust to the length of the nanoflake and the electrode material, showing great application potential. Those findings may throw light on the development of spintronic devices. 相似文献
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Megha Sen Chowdhury Dr. Selcuk Gumus Dr. Sanchari Dasgupta Dr. Ishani Majumder Dr. Abir Bhattacharya Dr. Debasis Das Dr. Jayanta Mukhopadhyay Dr. Debosreeta Bose Dr. Saumya Dasgupta Dr. Yuksel Akinay Dr. Madhumita Mukhopadhyay 《ChemistryOpen》2022,11(6):e202200033
We report, for the first time, a detailed crystallographic study of the supramolecular arrangement for a set of zinc(II) Schiff base complexes containing the ligand 2,6-bis((E)-((2-(dimethylamino)ethyl)imino)methyl)-4-R-phenol], where R=methyl/tert-butyl/chloro. The supramolecular study acts as a pre-screening tool for selecting the compartmental ligand R of the Schiff base for effective binding with a targeted protein, bovine serum albumin (BSA). The most stable hexagonal arrangement of the complex [Zn − Me] (R=Me) stabilises the ligand with the highest FMO energy gap (ΔE=4.22 eV) and lowest number of conformations during binding with BSA. In contrast, formation of unstable 3D columnar vertebra for [Zn − Cl] (R=Cl) tend to activate the system with lowest FMO gap (3.75 eV) with highest spontaneity factor in molecular docking. Molecular docking analyses reported in terms of 2D LigPlot+ identified site A, a cleft of domains IB, IIIA and IIIB, as the most probable protein binding site of BSA. Arg144, Glu424, Ser428, Ile455 and Lys114 form the most probable interactions irrespective of the type of compartmental ligands R of the Schiff base whereas Arg185, Glu519, His145, Ile522 act as the differentiating residues with ΔG=−7.3 kcal mol−1. 相似文献
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Given a graph sequence denote by T3(Gn) the number of monochromatic triangles in a uniformly random coloring of the vertices of Gn with colors. In this paper we prove a central limit theorem (CLT) for T3(Gn) with explicit error rates, using a quantitative version of the martingale CLT. We then relate this error term to the well-known fourth-moment phenomenon, which, interestingly, holds only when the number of colors satisfies . We also show that the convergence of the fourth moment is necessary to obtain a Gaussian limit for any , which, together with the above result, implies that the fourth-moment condition characterizes the limiting normal distribution of T3(Gn), whenever . Finally, to illustrate the promise of our approach, we include an alternative proof of the CLT for the number of monochromatic edges, which provides quantitative rates for the results obtained in [7]. 相似文献
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