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 $G$ be a group and $S$ an inverse closed subset of $G\setminus \{1\}$. By a Cayley graph $Cay(G,S)$ we mean the graph whose vertex set is the set of elements of $G$ and two vertices $x$ and $y$Expand
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


On Isomorphisms of Finite Cayley Graphs
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
Spectra of Cayley graphs
  • L. Babai
  • Mathematics, Computer Science
  • J. Comb. Theory, Ser. B
  • 1979
The results are formulated for directed graphs with colored edges and the existence of k nonisomorphic Cayley graphs of Dp with the same spectrum provided p > 64k, prime is proved. Expand
Further restrictions on the structure of finite CI-groups
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
On isomorphisms of finite Cayley graphs--a survey
  • Caiheng Li
  • Computer Science, Mathematics
  • Discret. Math.
  • 2002
This article is devoted to surveying results, open problems and methods in the study of the isomorphism problem for Cayley graphs. Expand
The Cayley isomorphism property for groups of order 8p
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
The Cayley isomorphism property for groups of order p^3q
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 $8p$.
Character Theory of Finite Groups
Algebras, modules, and representations Group representations and characters Characters and integrality Products of characters Induced characters Normal subgroups T.I. sets and exceptional charactersExpand
Representations and Characters of Groups
Groups representations and characters book 1976. representation and characters of groups gordon james. representations and characters of groups by gordon james. representations and characters ofExpand
GAP -Groups, Algorithms, and Programming
  • 2008
Representations and Characters of Groups. Cambridge: Cambridge University Press. D ow nl oa de d by [ A lir ez a A bd ol la hi ] at 1 4: 09 2 4 A ug us t 2 01 5 CHARACTER SUMS FOR CAYLEY
  • 2001