Two-geodesic-transitive graphs which are locally self-complementary期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Two-geodesic-transitive graphs which are locally self-complementary

Institution:	1. School of Statistics, Jiangxi University of Finance and Economics, Nanchang, Jiangxi, 330013, PR China;2. School of Mathematics and Statistics, Central South University, Changsha, Hunan, 410075, PR China;3. Research Center of Applied Statistics, Jiangxi University of Finance and Economics, Nanchang, Jiangxi, 330013, PR China

Abstract:	A 2-geodesic of a graph is a vertex triple $(u, v, w)$ with v adjacent to both u and w, $u \neq w$ and $u, w$ are not adjacent. A graph is said to be 2-geodesic-transitive if its automorphism group is transitive on both the set of arcs and the set of 2-geodesics. In this paper, we first determine the family of 2-geodesic-transitive graphs which are locally self-complementary, and then classify the family of 2-geodesic-transitive graphs that the local subgraph induced by the neighbor of a vertex is an arc-transitive circulant.

Keywords:	Two-geodesic-transitive graph arc-Transitive graph Local subgraph Self-complementary
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