پديدآورندگان :
Ghaffarzadeh Mehdi gh.ghaffarzadeh@iaukhoy.ac.ir Department of Mathematics, Khoy Branch, Islamic Azad University, Khoy, Iran , Ghasemi Mohsen m.ghasemi@urmia.ac.ir Department of Mathematics, Urmia University, Urmia 57135, Iran , Lewis Mark L. lewis@math.kent.edu Department of Mathematical Sciences, Kent State University, Kent, OH 44242, United States
چكيده فارسي :
Let G be a finite group, and write cd(G) for the set of degrees of irreducible characters of G.
Th e common-divisor graph Г(G) associated to G is the graph whose vertex set is cd(G)nf1g and
there is an edge between distinct vertices a and b, if (a;b) 1. In this talk we prove that if G(G)
is a k-regular graph for some k ≥ 0, then for the solvable groups, either G(G) is a complete graph
of order k+1 or Г(G) has two connected components which are complete of the same order and
for the nonsolvable groups, either k = 0 and cd(G) = cd(PSL2(2f )), where f ≥ 2 or Г(G) is a
4-regular graph with 6 vertices and cd(G) = cd(Alt7) or cd(Sym7).
