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101.
Jakub Przybyło 《Random Structures and Algorithms》2015,47(4):776-791
Consider a simple graph G = (V,E) and its proper edge colouring c with the elements of the set {1,2,…,k}. The colouring c is said to be neighbour sum distinguishing if for every pair of vertices u, v adjacent in G, the sum of colours of the edges incident with u is distinct from the corresponding sum for v. The smallest integer k for which such colouring exists is known as the neighbour sum distinguishing index of a graph and denoted by . The definition of this parameter, which makes sense for graphs containing no isolated edges, immediately implies that , where Δ is the maximum degree of G. On the other hand, it was conjectured by Flandrin et al. that for all those graphs, except for C5. We prove this bound to be asymptotically correct by showing that . The main idea of our argument relays on a random assignment of the colours, where the choice for every edge is biased by so called attractors, randomly assigned to the vertices. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 776–791, 2015 相似文献
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Let G be a graph with vertex set V(G) and edge set E(G). A labeling f : V(G) →Z2 induces an edge labeling f*: E(G) → Z2 defined by f*(xy) = f(x) + f(y), for each edge xy ∈ E(G). For i ∈ Z2, let vf(i) = |{v ∈ V(G) : f(v) = i}| and ef(i) = |{e ∈ E(G) : f*(e) =i}|. A labeling f of a graph G is said to be friendly if |vf(0)- vf(1)| ≤ 1. The friendly index set of the graph G, denoted FI(G), is defined as {|ef(0)- ef(1)|: the vertex labeling f is friendly}. This is a generalization of graph cordiality. We investigate the friendly index sets of cyclic silicates CS(n, m). 相似文献
104.
An all-to-all routing in a graph G is a set of oriented paths of G, with exactly one path for each ordered pair of vertices. The load of an edge under an all-to-all routing R is the number of times it is used (in either direction) by paths of R, and the maximum load of an edge is denoted by . The edge-forwarding index is the minimum of over all possible all-to-all routings R, and the arc-forwarding index is defined similarly by taking direction into consideration, where an arc is an ordered pair of adjacent vertices. Denote by the minimum number of colours required to colour the paths of R such that any two paths having an edge in common receive distinct colours. The optical index is defined to be the minimum of over all possible R, and the directed optical index is defined similarly by requiring that any two paths having an arc in common receive distinct colours. In this paper we obtain lower and upper bounds on these four invariants for 4-regular circulant graphs with connection set , . We give approximation algorithms with performance ratio a small constant for the corresponding forwarding index and routing and wavelength assignment problems for some families of 4-regular circulant graphs. 相似文献
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106.
Yuan Shan 《数学学报(英文版)》2015,31(11):1725-1738
In this paper, we study the nonperiodic first-order Hamiltonian system ù = J L(t)u +J H(t, u), where H ∈ C1(R × R2n). With some assumptions on L, the corresponding Hamiltonian operator has only discrete spectrum. By using the index theory for self-adjoint operator equation,we establish the existence of multiple homoclinic orbits for the asymptotically quadratic nonlinearty satisfying some twist conditions between infinity and origin. 相似文献
107.
Multi-address coding (MAC) lidar is a novel lidar system recently developed by our laboratory. By applying a new combined technique of multi-address encoding, multiplexing and decoding, range resolution is effectively improved. In data processing, a signal enhancement method involving laser signal demodulation and wavelet de-noising in the downlink is proposed to improve the signal to noise ratio (SNR) of raw signal and the capability of remote application. In this paper, the working mechanism of MAC lidar is introduced and the implementation of encoding and decoding is also illustrated. We focus on the signal enhancement method and provide the mathematical model and analysis of an algorithm on the basis of the combined method of demodulation and wavelet de-noising. The experimental results and analysis demonstrate that the signal enhancement approach improves the SNR of raw data. Overall, compared with conventional lidar system, MAC lidar achieves a higher resolution and better de-noising performance in long-range detection. 相似文献
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针对电子系统中多值测试条件下的测试排序问题,提出了一种诊断策略优化方法。首先,以相关性矩阵模型为基础,将已有的二值测试的优化算法同多值测试问题相结合,提出了适用于多值测试的基于霍夫曼编码的启发式函数;其次,将平均测试代价最小和平均测试步骤最少作为优化目标,采用与或树启发式搜索算法生成诊断树,得到多值测试的诊断策略,并给出了诊断策略优化方法的具体实现步骤;最后,将其应用到航空设备的实例中。结果表明提出的基于霍夫曼编码的与或树启发式搜索算法是可行的,其生成的诊断树是最优的,比基于信息熵的与或树启发式搜索算法具有更小的平均测试代价和更少的平均测试步骤。 相似文献