Abstract
Let X = ( V , E ) be a connected graph and S ⊆ E . S is said to be an m -restricted edge cut if X - S is disconnected and each component of X - S contains at least m vertices. Let λ ( m ) ( X ) be the minimum size of all m-restricted edge cuts, and ξ m ( X ) = min { ω ( U ) : U ⊆ V , | U | = m and X [ U ] is connected } , where ω ( U ) is the number of edges with one end in U and the other end in V ⧹ U , X [ U ] is the subgraph of X induced by U. A graph X is said to be optimally- λ ( 3 ) if λ ( i ) ( X ) = ξ i ( X ) ( i = 1 , 2 , 3 ) . In this paper, optimally- λ ( 3 ) vertex-transitive graphs are studied. In particular, generating sets of optimally- λ ( 3 ) minimal Cayley graphs are completely characterized.
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.
