On Isomorphic 4-Regular Circulant Graphs (Contributo in atti di convegno)

Type
Label
  • On Isomorphic 4-Regular Circulant Graphs (Contributo in atti di convegno) (literal)
Anno
  • 2006-01-01T00:00:00+01:00 (literal)
Alternative label
  • NICOLOSO Sara; PIETROPAOLI Ugo (2006)
    On Isomorphic 4-Regular Circulant Graphs
    in ISMP 2006 - International Symposium on MathematicalISMP 2006 - International Symposium on MathematicalProgramming, Rio de Janeiro, Brazil, 30 Luglio - 4 Agosto 2006
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • NICOLOSO Sara; PIETROPAOLI Ugo (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • NICOLOSO Sara, IASI-CNR; PIETROPAOLI Ugo, Università di Roma Tor Vergata (literal)
Titolo
  • On Isomorphic 4-Regular Circulant Graphs (literal)
Abstract
  • Consider three integers $n,a,b$ such that $n>0$, $a \neq 0$, and $b \neq 0$. The simple undirected graph $C_n(a,b)=(V,E)$ where $V = \{v_0, v_1, \dots, v_{n-1}\}$ and $E = \{(v_i,v_{(i+a)\bmod n})$, $ (v_i,v_{(i+b)\bmod n})$, for $i=0, \dots, n-1 )\}$ is called circulant graph. In this contribution we shall consider only circulant graphs which are 4-regular and connected. We define a simple combinatorial model for the graphs, and investigate on some characteristic cycles of them. We propose a necessary and sufficient condition for two graphs in this class to be isomorphic. The result shows that the \'Ad\'am conjecture is true on the studied class of 4-regular and connected circulant graphs. The condition can also be used to easily generate all the circulant graphs isomorphic to a given one. (literal)
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