4.7 Article

On diameter two Cayley graphs

Journal

APPLIED MATHEMATICS AND COMPUTATION
Volume 434, Issue -, Pages -

Publisher

ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2022.127437

Keywords

Cayley graph; Diameter; Vertex -transitive

Funding

  1. NSFC [12061034]
  2. NSFHN [2022JJ30674]
  3. NSFJX [20212BAB201010]
  4. CPSF [2022M711424]

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This paper investigates the properties of Cayley graphs and proves that there exist Cayley graphs satisfying certain conditions for specific positive integers m and k, where the automorphism group exhibits different levels of transitivity on different subsets.
Let X be a Cayley graph whose diameter is 2. Set R := Aut(X) and w is an element of V(X). In this paper, it is shown that: for every positive integer m at least 6, there is a such Cayley graph X of m points such that R-w acts transitively in X-2(w ) but not in X(w); for every positive integer k at least 3, there is a such graph X of valency k such that Rw is transitive in X-2(w ) but not in X(w). (C) 2022 Elsevier Inc. All rights reserved.

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