Abstract
Let D ( G ) = ( d i , j ) n × n denote the distance matrix of a connected graph G with order n , where d i j is equal to the distance between v i and v j in G . The largest eigenvalue of D ( G ) is called the distance spectral radius of graph G , denoted by ϱ ( G ) . In this paper, some graft transformations that decrease or increase ϱ ( G ) are given. With them, for the graphs with both order n and k pendant vertices, the extremal graphs with the minimum distance spectral radius are completely characterized; the extremal graph with the maximum distance spectral radius is shown to be a dumbbell graph (obtained by attaching some pendant edges to each pendant vertex of a path respectively) when 2 ≤ k ≤ n − 2 ; for k = 1 , 2 , 3 , n − 1 , the extremal graphs with the maximum distance spectral radius are completely characterized.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: 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.