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2.
Jim Foster 《Journal of Combinatorial Theory, Series A》2007,114(8):1515-1525
We show that for an n-gon with unit diameter to have maximum area, its diameter graph must contain a cycle, and we derive an isodiametric theorem for such n-gons in terms of the length of the cycle. We then apply this theorem to prove Graham's 1975 conjecture that the diameter graph of a maximal 2m-gon (m?3) must be a cycle of length 2m−1 with one additional edge attached to it. 相似文献
3.
关于环网G(N;S1,S2)的直径 总被引:6,自引:0,他引:6
本文首先给出了环网G(N;s_1,s_2)存在有限直径的充要条件;用初等数论方法给出了其直径的简明计算公式;最后讨论了类似文献[3]的环网直径的对偶性问题. 相似文献
4.
A subset S of the vertex set of a graph G is called acyclic if the subgraph it induces in G contains no cycles. S is called an acyclic dominating set of G if it is both acyclic and dominating. The minimum cardinality of an acyclic dominating set, denoted by γa(G), is called the acyclic domination number of G. Hedetniemi et al. [Acyclic domination, Discrete Math. 222 (2000) 151-165] introduced the concept of acyclic domination and posed the following open problem: if δ(G) is the minimum degree of G, is γa(G)?δ(G) for any graph whose diameter is two? In this paper, we provide a negative answer to this question by showing that for any positive k, there is a graph G with diameter two such that γa(G)-δ(G)?k. 相似文献
5.
Soraya A. Khodier 《Optics & Laser Technology》2004,36(1):355-67
A combined interference and diffraction pattern, in the form of equidistant interference fringes, resulting from illuminating a vertical metallic wire by a laser beam is analyzed to measure the diameter of four standard wires. The diameters range from 170 to 450 μm. It is found that the error in the diameter measurements increases for small metallic wires and for small distances between the wire and the screen due to scattering effects. The intensity of the incident laser beam was controlled by a pair of sheet polaroids to minimize the scattered radiation. The used technique is highly sensitive, but requires controlled environmental conditions and absence of vibration effects. The expanded uncertainty for k=2 is calculated and found to decrease from U(D)=±1.45 μm for the wire of nominal diameter 170 μm to ±0.57 μm for the diameter 450 μm. 相似文献
6.
We construct a family of finite 2-groups which have commuting graph of increasing diameter. 相似文献
7.
对于任意的正数M以及正整数d≥4,存在直径为d的i-边连通无环图G使得ζ(G)≥M,其中ζ(G)是G的Betti亏数,i=1,2,3。 相似文献
8.
9.
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
10.
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