ABSTRACT
Let be the family of graphs with n vertices and with the matching number β. The distance signless Laplacian spectral radius of a graph G is denoted by . Li and Sun (Matching number, connectivity and eigenvalues of distance signless Laplacians. Linear Multilinear Algebra, 2019. https://doi.org/10.1080/03081087.2019.1588218) proved that if , for any , with equality if and only if . Further Li and Sun conjectured that if , the statement holds. In this paper, we disprove this conjecture by an example, when n = 19 and . Further by using a different technique, we show that the statement holds for .
2010 Mathematics Subject Classification:
Disclosure statement
No potential conflict of interest was reported by the authors.