Character Sums for Cayley Graphs

  title={Character Sums for Cayley Graphs},
  author={Alireza Abdollahi and Maysam Zallaghi},
  journal={Communications in Algebra},
  pages={5159 - 5167}
Following [1], by a Cayley digraph we mean a graph Cay(G, S) whose vertex set is a group G, and there exists a directed edge from a vertex g to another vertex h if g −1 h ∈ S, where S is a generating subset of G. The graph Cay(G, S) is called a Cayley graph if S = S −1 and 1 ∉ S. In Problem 3.3 of the above cited article, the following question is proposed. Let G be a finite group, let Γ = Cay(G, S) be a Cayley digraph, ν a positive integer, and where χ1, …, χ h are all irreducible characters… Expand
Non-Abelian finite groups whose character sums are invariant but are not Cayley isomorphism
Let [Formula: see text] be a group and [Formula: see text] an inverse closed subset of [Formula: see text]. By a Cayley graph [Formula: see text], we mean the graph whose vertex set is the set ofExpand
The lit-only σ-game is a nondeterministic linear dynamical process whose local transition rule is specified by a digraph. The player of the game can choose among several possible transitions at eachExpand


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It is shown that a nonabelian simple group has the 4-CI property if and only if it is A5, and that no nonabelians simple groups has the 5- CI property. Expand
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A group G is called a CI-group if, for any subsets S,T⊂ G, whenever two Cayley graphs Cay(G,S) and Cay(G,T) are isomorphic, there exists an element σ∊Aut(G) such that Sσ = T. The problem of seekingExpand
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For every prime p > 3, it is proved that Q x Z_p is a DCI-group, which completes the description of CI-groups of order 8p. Expand
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For every prime $p>3$ we prove that $Q \times \mathbb{Z}_p$ and $\mathbb{Z}_2^3 \times \mathbb{Z}_p$ are DCI- groups. This result completes the description of CI-groups of order $8p$.
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