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951.
952.
In this paper,it is shown that for a 3-dimensional small cover M over a polytope P,there are only 2-torsions in H1(M;Z).Moreover,the mod 2 Betti number growth of finite covers of M is studied. 相似文献
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介绍了Rieffel定义的紧致量子度量空间与量子Gromov-Hausdorff距离和近来Latrémolière定义的量子Gromov-Hausdorff邻距,分别讨论了矩阵代数如何在这两种量子距离下收敛至球面. 相似文献
956.
A drawing of a graph is pseudolinear if there is a pseudoline arrangement such that each pseudoline contains exactly one edge of the drawing. The pseudolinear crossing number of a graph G is the minimum number of pairwise crossings of edges in a pseudolinear drawing of G. We establish several facts on the pseudolinear crossing number, including its computational complexity and its relationship to the usual crossing number and to the rectilinear crossing number. This investigation was motivated by open questions and issues raised by Marcus Schaefer in his comprehensive survey of the many variants of the crossing number of a graph. 相似文献
957.
A weighted (unweighted) graph is called equiarboreal if the sum of weights (the number) of spanning trees containing a given edge in is independent of the choice of edge. In this paper, we give some resistance characterizations of equiarboreal weighted and unweighted graphs, and obtain the necessary and sufficient conditions for -subdivision graphs, iterated double graphs, line graphs of regular graphs and duals of planar graphs to be equiarboreal. Applying these results, we obtain new infinite families of equiarboreal graphs, including iterated double graphs of 1-walk-regular graphs, line graphs of triangle-free 2-walk-regular graphs, and duals of equiarboreal planar graphs. 相似文献
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960.
Toll convexity is a variation of the so-called interval convexity. A tolled walk between two non-adjacent vertices and in a graph is a walk, in which is adjacent only to the second vertex of and is adjacent only to the second-to-last vertex of . A toll interval between is a set . A set is toll convex, if for all . A toll closure of a set is the union of toll intervals between all pairs of vertices from . The size of a smallest set whose toll closure is the whole vertex set is called a toll number of a graph , . The first part of the paper reinvestigates the characterization of convex sets in the Cartesian product of two graphs. It is proved that the toll number of the Cartesian product of two graphs equals 2. In the second part, the toll number of the lexicographic product of two graphs is studied. It is shown that if is not isomorphic to a complete graph, . We give some necessary and sufficient conditions for . Moreover, if has at least two extreme vertices, a complete characterization is given. Furthermore, graphs with are characterized. Finally, the formula for is given — it is described in terms of the so-called toll-dominating triples or, if is complete, toll-dominating pairs. 相似文献