چكيده به لاتين
Abstract
The power graph TG of a finite group G is the graph whose vertex set is the group,
two distinct elements being adjacent if one is a power of the other. In this thesis, we
classify finite groups G for which the genus of TG is one. Also a characterization of
X(TG) is presented . Moreover , we classify all finite groups whose power graphs are
uniquely colorable , split or unicyclic.
Keywords: power graph, finite group , genus, graph , coloring , spilit graphs ,
unicyclic graph.
