Abstract
ABSTRACT Let G be a connected graph with distance matrix , and let be the diagonal matrix of vertex transmissions of G. For any , the -matrix of G is defined as In this paper, we study the -spectra of graphs. Firstly, the -eigenvalues of some special graphs are presented. Then we give a lower bound on the kth smallest -eigenvalue of graphs, and the extremal graphs are characterized. Also, several graph transformations on the -spectral radius are given, as applications, some extremal graphs with given structure parameters are characterized. Finally, we give some properties when two graphs have the same -spectra and several graphs are proved to be determined by their -spectra.
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.
