Ordering graphs with given size by their signless Laplacian spectral radii
The authors of this paper investigate the signless Laplacian spectral radius \(q(G)\) of a graph \(G\). They first give an upper bound on \(q(G)\) with fixed size and maximum degree. Further, applying this upper bound, they order graphs by their signless Laplacian spectral radii with respect to the maximum degree. As an application, the first \(\lfloor d/2 \rfloor\) graphs with the largest signless Laplacian spectral radius among all graphs with fixed size and diameter \(d\) are determined.
scientific article; zbMATH DE number 7596041
scientific article