Abstract
ABSTRACT The Randić matrix (short for R-matrix) of a graph G is a symmetric matrix whose -entry is equal to if , and 0 otherwise. The R-eigenvalues of a graph G are the eigenvalues of its Randić matrix R. In this paper, we introduce the star complements of R-matrix of a graph G, especially of a tree T, from which we investigate the R-eigenvalues of T. First, if a tree T has a R-eigenvalue ρ with multiplicity k, then whenever . Second, a tree T has at least k+1 pendant edges form an induced matching if it has as a R-eigenvalue with multiplicity k. Finally, we determine the trees with a non-zero R-eigenvalue of maximal possible multiplicity.
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.
