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   Seminário de Teoria da Computação e Combinatória (TCC)

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Título:      Unitary Cayley Graphs
            
Palestrante: Daniel Alejandro Jaume
             Universidad Nacional de San Luis

Hora e Data: 14h, sexta-feira, 30 de setembro de 2011

Local:       auditório do NUMEC

Resumo:

For a positive integer n>1 the "unitary Cayley graph"
         
    X_n = Cay(Z_n,U_n) 

is defined by the additive group of the ring Z_n of integers
modulo n and the multiplicative group U_n of its units. If
we represent the elements of Z_n by the integers 0,1,...,n-1
then it is well known that

    U_n = {a \in Z_n : gcd(a,n)=1}

So X_n has vertex set V(X_n)=Z_n= {0,1,...,n-1} and edge set

    E(X_n) = {{a,b} : a,b \in Z_n, gcd(a-b,n)=1}

Unitary Cayley  graphs are highly symmetric.  They have some
remarkable  properties connecting  graph  theory and  number
theory.   Cayley  graphs model  a  wide  array of  symmetric
networks of  theoretical and practical  interest. Properties
established for  all, or  for certain subclasses  of, Cayley
graphs are useful.