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41.
Xiang-En Chen 《数学研究通讯:英文版》2016,32(4):359-374
Let G be a simple graph. A total coloring f of G is called an E-total coloring if no two adjacent vertices of G receive the same color, and no edge of G receives the same color as one of its endpoints. For an E-total coloring f of a graph G and any vertex x of G, let C(x) denote the set of colors of vertex x and of the edges incident with x, we call C(x) the color set of x. If C(u)≠ C(v) for any two different vertices u and v of V(G), then we say that f is a vertex-distinguishing E-total coloring of G or a VDET coloring of G for short. The minimum number of colors required for a VDET coloring of G is denoted by χ_(vt)~e(G) and is called the VDET chromatic number of G. The VDET coloring of complete bipartite graph K_(7,n)(7 ≤ n ≤ 95) is discussed in this paper and the VDET chromatic number of K_(7,n)(7 ≤ n ≤ 95) has been obtained. 相似文献
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The concept of a perfect coloring, introduced by P. Delsarte, generalizes the concept of completely regular code. We study the perfect 3-colorings (also known as the equitable partitions into three parts) on 6-regular graphs of order 9. A perfect n-colorings of a graph is a partition of its vertex set. It splits vertices into n parts A1, A2,...,An such that for all i,j∈{1,2,...,n}, each vertex of Ai is adjacent to aij vertices of Aj. The matrix A =(aij)n×n is called quotient matrix or parameter matrix. In this article, we start by giving an algorithm to find all different types of 6-regular graphs of order 9. Then, we classify all the realizable parameter matrices of perfect 3-colorings on 6-regular graphs of order 9. 相似文献
44.
Animesh K. Ojha Sunil K. Srivastava S. Schlücker W. Kiefer B. P. Asthana Ranjan K. Singh 《Journal of Raman spectroscopy : JRS》2007,38(12):1656-1664
A concentration‐dependent Raman study of the ν(C Br) stretching and trigonal bending modes of 2‐ and 3‐Br‐pyridine (2Br‐p and 3Br‐p) in CH3OH was performed at different mole fractions of the reference molecule, 2Br‐p/3Br‐p, from 0.1 to 0.9 in order to understand the origin of blue/red wavenumber shifts of the vibrational modes due to hydrogen‐bond formation. The appearance of additional Raman bands in these binary systems at ∼617 cm−1in the case of 2Br‐p and at ∼618 cm−1 in the case of 3Br‐p compared to neat bromopyridine derivatives were attributed to specific hydrogen‐bonded complexes formed in the mixtures. The interpretation of experimental results is supported by density functional calculations on optimized geometries and vibrational wavenumbers of 2Br‐p and 3Br‐p and a series of hydrogen‐bonded complexes with methanol. The parameters obtained from these calculations were used for a qualitative explanation of the blue/red shifts. The wavenumber shifts and linewidth changes for the ν(C Br) stretching and trigonal bending modes as a function of concentration reveal that the caging effects leading to motional narrowing and diffusion‐causing line broadening are simultaneously operative, in addition to the blue shift caused due to hydrogen bonding. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
45.
We give new bounds on the star arboricity and the caterpillar arboricity of planar graphs with given girth. One of them answers an open problem of Gyárfás and West: there exist planar graphs with track number 4. We also provide new NP-complete problems. 相似文献
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蒙特卡罗方法计算定积分的进一步讨论 总被引:3,自引:0,他引:3
介绍了蒙特卡罗方法计算定积分的原理和方法.给出了用蒙特卡罗方法计算定积分的一个简单证明,从而揭示了蒙特卡罗方法和定积分定义间的内在联系.针对蒙特卡罗方法收敛慢的特点,提出将蒙特卡罗方法与相应的数值计算方法相结合,提高计算结果的精度.此外,将蒙特卡罗方法推广到反常积分上去. 相似文献
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We analyse the mixing time of Markov chains using path coupling with stopping times. We apply this approach to two hypergraph problems. We show that the Glauber dynamics for independent sets in a hypergraph mixes rapidly as long as the maximum degree Δ of a vertex and the minimum size m of an edge satisfy m ≥ 2Δ + 1. We also show that the Glauber dynamics for proper q‐colorings of a hypergraph mixes rapidly if m ≥ 4 and q > Δ, and if m = 3 and q ≥ 1.65Δ. We give related results on the hardness of exact and approximate counting for both problems. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2008 相似文献
50.
Xuding Zhu 《Journal of Graph Theory》2008,59(4):261-278
This article proves the following result: Let G and G′ be graphs of orders n and n′, respectively. Let G* be obtained from G by adding to each vertex a set of n′ degree 1 neighbors. If G* has game coloring number m and G′ has acyclic chromatic number k, then the Cartesian product G□G′ has game chromatic number at most k(k + m ? 1). As a consequence, the Cartesian product of two forests has game chromatic number at most 10, and the Cartesian product of two planar graphs has game chromatic number at most 105. © 2008 Wiley Periodicals, Inc. J Graph Theory 59: 261–278, 2008 相似文献