On graphs with a few distinct reciprocal distance Laplacian eigenvalues

Abstract

For a $ \nu $-vertex connected graph $ \Gamma $, we consider the reciprocal distance Laplacian matrix defined as $ RD^L(\Gamma) = RT(\Gamma)-RD(\Gamma) $, i.e., $ RD^L(\Gamma) $ is the difference between the diagonal matrix of the reciprocal distance degrees $ RT(\Gamma) $ and the Harary matrix $ RD(\Gamma) $. In this article, we determine the graphs with exactly two distinct reciprocal distance Laplacian eigenvalues.We completely characterize the graph classes with a $ RD^L $ eigenvalue of multiplicity $ \nu-2 $. Moreover, we characterize families of graphs with reciprocal distance Laplacian eigenvalue whose multiplicity is $ \nu-3 $.

Keywords

• harrary matrix
• reciprocal distance laplacian matrix
• reciprocal distance laplacian eigenvalues