On connected components and perfect codes of proper order graphs of finite groups
H Li,
S Lin,
X Ma
Abstract:Let G be a finite group with the identity element e. The proper order graph of G, denoted by S * (G), is an undirected graph with a vertex set G \ {e}, where two distinct vertices x and y are adjacent whenever o(x) | o(y) or o(y) | o(x), where o(x)and o(y) are the orders of x and y, respectively. This paper studies the perfect codes of S * (G). We characterize all connected components of a proper order graph and give a necessary and sufficient condition for a connected proper order graph. We also determine the… Show more
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