Abstract
As a classic problem of spectral graph theory, Brualdi-Solheid problem asks which graph achieves the extremal (maximum or minimum) spectral radius for a given class of graphs. In this paper, we focus on this problem for graphs with fixed independence number. We first obtain the maximum spectral radius and unique extremal graph among all bipartite graphs of order n with independence number α. Secondly, we study the minimum spectral radius of graphs with fixed independence number. Let Gn,α be the set of connected graphs of order n with independence number α. We show that tree has the minimum spectral radius over all graphs in Gn,α provided that α≥⌈n2⌉, and determine all the extremal graphs in Gn,n−4.
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.
