2,516 research outputs found
The Erd\H{o}s-Ko-Rado theorem for twisted Grassmann graphs
We present a "modern" approach to the Erd\H{o}s-Ko-Rado theorem for
Q-polynomial distance-regular graphs and apply it to the twisted Grassmann
graphs discovered in 2005 by van Dam and Koolen.Comment: 5 page
A new near octagon and the Suzuki tower
We construct and study a new near octagon of order which has its
full automorphism group isomorphic to the group and which
contains copies of the Hall-Janko near octagon as full subgeometries.
Using this near octagon and its substructures we give geometric constructions
of the -graph and the Suzuki graph, both of which are strongly
regular graphs contained in the Suzuki tower. As a subgeometry of this octagon
we have discovered another new near octagon, whose order is .Comment: 24 pages, revised version with added remarks and reference
Resolving sets for Johnson and Kneser graphs
A set of vertices in a graph is a {\em resolving set} for if, for
any two vertices , there exists such that the distances . In this paper, we consider the Johnson graphs and Kneser
graphs , and obtain various constructions of resolving sets for these
graphs. As well as general constructions, we show that various interesting
combinatorial objects can be used to obtain resolving sets in these graphs,
including (for Johnson graphs) projective planes and symmetric designs, as well
as (for Kneser graphs) partial geometries, Hadamard matrices, Steiner systems
and toroidal grids.Comment: 23 pages, 2 figures, 1 tabl
Measuring and Understanding Throughput of Network Topologies
High throughput is of particular interest in data center and HPC networks.
Although myriad network topologies have been proposed, a broad head-to-head
comparison across topologies and across traffic patterns is absent, and the
right way to compare worst-case throughput performance is a subtle problem.
In this paper, we develop a framework to benchmark the throughput of network
topologies, using a two-pronged approach. First, we study performance on a
variety of synthetic and experimentally-measured traffic matrices (TMs).
Second, we show how to measure worst-case throughput by generating a
near-worst-case TM for any given topology. We apply the framework to study the
performance of these TMs in a wide range of network topologies, revealing
insights into the performance of topologies with scaling, robustness of
performance across TMs, and the effect of scattered workload placement. Our
evaluation code is freely available
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