A 2-geodesic of a graph is a vertex triple (u, v, w) with vadjacent to both uand w, u not equal w and u, ware 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. (C) 2022 Elsevier B.V. All rights reserved.
机构:
Kobe Univ, Dept Math & Informat, Fac Human Dev, Kobe, Hyogo 6578501, JapanYokohama Natl Univ, Dept Math, Fac Educ & Human Sci, Yokohama, Kanagawa 2408502, Japan
Shirakura, Teruhiro
Tazawa, Shinsei
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机构:
Kinki Univ, Dept Math, Fac Sci & Engn, Higashiosaka, Osaka 5778502, JapanYokohama Natl Univ, Dept Math, Fac Educ & Human Sci, Yokohama, Kanagawa 2408502, Japan