Abstract
Nikiforov [The spectral radius of graphs without paths and cycles of specified length. Linear Algebra Appl. 2010;432(9):2243–2256] conjectured that for a given integer k, any graph G of sufficiently large order n with spectral radius contains all trees of order 2k+2, unless , where denotes the join of a complete graph of order k and an empty graph of order n−k. In this article, we show that the conjecture is true for trees of diameter at most four, more specifically, we prove that, for and , every graph G of order n with contains all trees T of order 2k+2 and of diameter at most four as a subgraph, unless .
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.