Finite 2-Geodesic Transitive Graphs of Prime Valency

Alice Devillers; W. Jin; Cai-Heng Li; Cheryl Praeger

doi:10.1002/jgt.21835

Finite 2-Geodesic Transitive Graphs of Prime Valency

Alice Devillers, W. Jin, Cai-Heng Li, Cheryl Praeger

Research output: Contribution to journal › Article › peer-review

27 Citations (Scopus)

Abstract

© 2014 Wiley Periodicals, Inc. Abstract We classify noncomplete prime valency graphs satisfying the property that their automorphism group is transitive on both the set of arcs and the set of 2-geodesics. We prove that either Γ is 2-arc transitive or the valency p satisfies p≡1 (mod 4), and for each such prime there is a unique graph with this property: it is a nonbipartite antipodal double cover of the complete graph Kp+1 with automorphism group PSL(2, p) × Z2 and diameter 3.

Original language	English
Pages (from-to)	18-27
Journal	Journal of Graph Theory
Volume	80
Issue number	1
DOIs	https://doi.org/10.1002/jgt.21835
Publication status	Published - 2015

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10.1002/jgt.21835

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abstract = "{\textcopyright} 2014 Wiley Periodicals, Inc. Abstract We classify noncomplete prime valency graphs satisfying the property that their automorphism group is transitive on both the set of arcs and the set of 2-geodesics. We prove that either Γ is 2-arc transitive or the valency p satisfies p≡1 (mod 4), and for each such prime there is a unique graph with this property: it is a nonbipartite antipodal double cover of the complete graph Kp+1 with automorphism group PSL(2, p) × Z2 and diameter 3.",

author = "Alice Devillers and W. Jin and Cai-Heng Li and Cheryl Praeger",

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AU - Li, Cai-Heng

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PY - 2015

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N2 - © 2014 Wiley Periodicals, Inc. Abstract We classify noncomplete prime valency graphs satisfying the property that their automorphism group is transitive on both the set of arcs and the set of 2-geodesics. We prove that either Γ is 2-arc transitive or the valency p satisfies p≡1 (mod 4), and for each such prime there is a unique graph with this property: it is a nonbipartite antipodal double cover of the complete graph Kp+1 with automorphism group PSL(2, p) × Z2 and diameter 3.

AB - © 2014 Wiley Periodicals, Inc. Abstract We classify noncomplete prime valency graphs satisfying the property that their automorphism group is transitive on both the set of arcs and the set of 2-geodesics. We prove that either Γ is 2-arc transitive or the valency p satisfies p≡1 (mod 4), and for each such prime there is a unique graph with this property: it is a nonbipartite antipodal double cover of the complete graph Kp+1 with automorphism group PSL(2, p) × Z2 and diameter 3.

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DO - 10.1002/jgt.21835

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JO - Journal of Graph Theory

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Finite 2-Geodesic Transitive Graphs of Prime Valency

Abstract

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