Two-geodesic-transitive graphs which are locally connected

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• 作者：Wei Jin ^{jinwei@jxufe.edu.cn}
• 关键词：Two-geodesic-transitive graph ; Quasiprimitive permutation group ; Automorphism group
• 刊名：Discrete Mathematics
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：340
• 期：4
• 页码：637-643
• 全文大小：425 K
• 卷排序：340

文摘

We investigate the family of 22-geodesic-transitive graphs which are locally connected. Let ΓΓ be such a graph. It is first shown that: for any integer d≥2d≥2, there exists such a ΓΓ of diameter dd; for any integer k≥3k≥3, there exists such a ΓΓ of valency kk unless kk is a prime and k≡3(mod4). Next, we completely determine the family of 22-geodesic-transitive graphs which are locally isomorphic to mCn¯ for some m≥1,n≥3m≥1,n≥3. Finally, we give a reduction result for the family of locally connected (G,2)(G,2)-geodesic-transitive graphs.