Abstract
A cut vertex of a graph is a vertex whose removal causes the resulting graph to have more connected components. We show that the prime divisor character degree graph of a solvable group has at most one cut vertex. We also prove that a solvable group whose prime divisor character degree graph has a cut vertex has at most two normal nonabelian Sylow subgroups. We determine the structures of those solvable groups whose prime divisor character degree graph has a cut vertex and has two normal nonabelian Sylow subgroups. Finally, we characterize a subgroup determined by the prime associated with the cut vertex in terms of the structure of the prime divisor character degree graph.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
