JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (10): 59-65.doi: 10.6040/j.issn.1671-9352.0.2022.004

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Ramanujan unitary one-matching bi-Cayley graphs over finite commutative rings

GOU Xiao-li, WANG Wei-zhong*   

  1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Published:2022-10-06

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Abstract: Let R be a finite commutative ring with unit element 1≠0, and let GR=BC(R; R×, R×, {0})denote the one-matching bi-Cayley graph over R, where R× is the set of units of R. A k-regular graph G is called a Ramanujan graph if any eigenvalue λ of G with |λ|≠k satisfies |λ|≤2(k-1)1/2. A necessary and sufficient condition for GR and its line graph to be Ramanujan is given.

Key words: unitary one-matching bi-Cayley graph, line graph, local ring, finite commutative ring, Ramanujan graph

CLC Number: 

  • O157.5
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