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11.
一类新的直径为4的整树 总被引:1,自引:0,他引:1
徐大申 《河北大学学报(自然科学版)》1997,(1)
本文给出了r为偶数,直径为4的树S(r,mi)为整树的一个充分条件。由此得到了r为偶数直径为4的整树S(r,mi)的一些新类,给出了它们的谱。同时表明这类整树有无穷多个。从而解决了文[4]中提出的有关直径为4整树的一个问题 相似文献
12.
We consider a class of graphs subject to certain restrictions, including the finiteness of diameters. Any surjective mapping φ:Γ→Γ′ between graphs from this class is shown to be an isomorphism provided that the following holds: Any two points of Γ are at a distance equal to the diameter of Γ if, and only if, their images are at a distance equal to the diameter of Γ′. This result is then applied to the graphs arising from the adjacency relations of spaces of rectangular matrices, spaces of Hermitian matrices, and Grassmann spaces (projective spaces of rectangular matrices). 相似文献
13.
We establish a Harnack inequality for finite connected graphs with non-negative Ricci curvature. As a consequence, we derive an eigenvalue lower bound, extending previous results for Ricci flat graphs. 相似文献
14.
Vojtech Blint 《Journal of Discrete Algorithms》2003,1(3-4):339-355
Let G be an undirected graph with two edge costs (c-cost and d-cost). We want to minimize the diameter of a spanning subgraph S (under d-cost) subject to the constraint that the total cost of the edges in S (with respect to c) does not exceed a given budget. We prove that this problem is non-approximable, even in some special cases. Similar results are proved if the stretch factor or the root stretch factor is considered instead of the diameter. 相似文献
15.
Measurement of diameter of metal cylinders using a sinusoidally vibrating interference pattern 总被引:1,自引:0,他引:1
A method for measuring external diameters of metal cylinders is proposed in which a sinusoidally vibrating interference pattern (SVIP) of 100-μm period is used as an exact scale. Lights from the end-points of a metal cylinder are extracted with a spatial filtering in an imaging system to form a cross-sectional image of the metal cylinder. On the image a sinusoidally phase-modulated signal owing to the SVIP is detected with a CCD image sensor to measure the phases of the SVIP at the two end-points of the cylinder. The coordinates of the two end-points are obtained from the phases at the two end-points, the phase distribution of the SVIP, and the coordinates of the pixels of the CCD image sensor. Metal cylinder diameters of 7.99, 8.00, and 9.00 mm are measured along their length directions with an error less than 1 μm. 相似文献
16.
Charles Audet Pierre Hansen Frédéric Messine 《Journal of Combinatorial Theory, Series A》2007,114(1):135-150
The convex octagon with unit diameter and maximum perimeter is determined. This answers an open question dating from 1922. The proof uses geometric reasoning and an interval arithmetic based global optimization algorithm to solve a series of non-linear and non-convex programs involving trigonometric functions. 相似文献
17.
本文给出了一种构造给定直径d和围长g的测地块的方法.它是文[1]中构造法的推广,解决了文[1]中待研究的几个问题.同时,对文[1]中的一个错误进行了修正. 相似文献
18.
We present two conjectures concerning the diameter of a direct power of a finite group. The first conjecture states that the diameter of Gn with respect to each generating set is at most n(|G|?rank(G)); and the second one states that there exists a generating set 𝒜, of minimum size, for Gn such that the diameter of Gn with respect to 𝒜 is at most n(|G|?rank(G)). We will establish evidence for each of the above mentioned conjectures. 相似文献
19.
Kexiang Xu 《Discrete Applied Mathematics》2011,159(15):1631-1640
The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. For a connected graph G=(V,E) and two nonadjacent vertices vi and vj in V(G) of G, recall that G+vivj is the supergraph formed from G by adding an edge between vertices vi and vj. Denote the Harary index of G and G+vivj by H(G) and H(G+vivj), respectively. We obtain lower and upper bounds on H(G+vivj)−H(G), and characterize the equality cases in those bounds. Finally, in this paper, we present some lower and upper bounds on the Harary index of graphs with different parameters, such as clique number and chromatic number, and characterize the extremal graphs at which the lower or upper bounds on the Harary index are attained. 相似文献
20.
Aguiló-Gost [New dense families of triple loop Networks, Discrete Math. 197/198 (1999) 15-27] has presented a new type of hyper-L tiles and used it to derive a new dense family of triple-loop networks. While Aguiló-Gost's hyper-L tile seems to be a promising tool for studying the triple-loop networks, we need to verify that the hyper-L tile producing good result is indeed the MDD of some triple-loop network. In this paper, we give necessary and sufficient conditions for the existence of Aguiló-Gost's hyper-L triple-loop networks and we correct some flaws in [F. Aguiló-Gost, New dense families of triple loop networks, Discrete Math. 197/198 (1999) 15-27]. 相似文献