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Ariane Carrance 《Random Structures and Algorithms》2019,55(3):615-648
We present here random distributions on (D + 1)‐edge‐colored, bipartite graphs with a fixed number of vertices 2p. These graphs encode D‐dimensional orientable colored complexes. We investigate the behavior of those graphs as p→∞. The techniques involved in this study also yield a Central Limit Theorem for the genus of a uniform map of order p, as p→∞. 相似文献
83.
《Discrete Mathematics》2019,342(10):2770-2782
“Which graphs are determined by their spectrum (DS for short)?” is a fundamental question in spectral graph theory. It is generally very hard to show a given graph to be DS and few results about DS graphs are known in literature. In this paper, we consider the above problem in the context of the generalized -spectrum. A graph is said to be determined by the generalized -spectrum (DGQS for short) if, for any graph , and have the same -spectrum and so do their complements imply that is isomorphic to . We give a simple arithmetic condition for a graph being DGQS. More precisely, let be a graph with adjacency matrix and degree diagonal matrix . Let be the signless Laplacian matrix of , and ( is the all-ones vector) be the -walk matrix. We show that if (which is always an integer) is odd and square-free, then is DGQS. 相似文献
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In the game of cops and robber, the cops try to capture a robber moving on the vertices of the graph. The minimum number of cops required to win on a given graph G is called the cop number of G. The biggest open conjecture in this area is the one of Meyniel, which asserts that for some absolute constant C, the cop number of every connected graph G is at most . In a separate paper, we showed that Meyniel's conjecture holds asymptotically almost surely for the binomial random graph. The result was obtained by showing that the conjecture holds for a general class of graphs with some specific expansion‐type properties. In this paper, this deterministic result is used to show that the conjecture holds asymptotically almost surely for random d‐regular graphs when d = d(n) ≥ 3. 相似文献
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E. Hitzer 《Mathematical Methods in the Applied Sciences》2011,34(12):1421-1429
This paper discusses the geometry of kD crystal cells given by (k+ 1) points in a projective space ?n+ 1. We show how the concepts of barycentric and fractional (crystallographic) coordinates, reciprocal vectors and dual representation are related (and geometrically interpreted) in the projective geometric algebra Cl(?n+ 1) (see (Die Ausdehnungslehre von 1844 und die Geom. Anal. Teubner: Leipzig, 1894)) and in the conformal algebra Cl(?n+ 1, 1). The crystallographic notions of d‐spacing, phase angle, structure factors, conditions for Bragg reflections, and the interfacial angles of crystal planes are obtained in the same context. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
90.
In the present paper, we introduce some new subclasses of meromorphic starlike,convex, close-to-convex and quasi-convex functions of β-reciprocal in terms of the linear operator using subordination. We obtain the coefficient estimates, convolution properties, integral preserving properties and inclusion relationships of the classes. The results presented here include several results as their special cases. 相似文献