On geodesic transitive graphs
On geodesic transitive graphs
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DOI：
10.1016/j.disc.2014.11.005
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发表时间：
2015-03
期刊：
影响因子：
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通讯作者：
W. Jin;Alice Devillers;Caiheng Li;C. Praeger
中科院分区：
文献类型：
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作者：
W. Jin;Alice Devillers;Caiheng Li;C. Praeger
本文的主要目的是研究图的三个对称性质：s-弧传递性，s-测地传递性和s-距离传递性之间的关系。韦斯的一个著名结果告诉我们，如果一个至少3度的图是s-弧传递的，则s≤ 7。我们证明了对于s≤ 3的每一个值，对于任意大的t值，有无穷多个s-弧传递图是t-测地传递的。当4≤ s≤ 7时，s-弧传递的测地传递图可以被显式地描述，并且除了两个图之外，所有的测地传递图都与经典的广义多边形有关。最后，我们表明，佩利图和Peisert图，这是已知的距离传递，几乎从来没有2-测地线传递，只有三个小的例外。
The main purpose of this paper is to investigate relationships between three graph symmetry properties: s-arc transitivity, s-geodesic transitivity, and s-distance transitivity. A well-known result of Weiss tells us that if a graph of valency at least 3 is s-arc transitive then s≤ 7. We show that for each value of s≤ 3, there are infinitely many s-arc transitive graphs that are t-geodesic transitive for arbitrarily large values of t. For 4≤ s≤ 7, the geodesic transitive graphs that are s-arc transitive can be explicitly described, and all but two of these graphs are related to classical generalized polygons. Finally, we show that the Paley graphs and the Peisert graphs, which are known to be distance transitive, are almost never 2-geodesic transitive, with just three small exceptions.