Laplacian Spectrum and Domination in Trees

Deepak Rajendraprasad, Durga R. Sankaranarayanan

For a finite simple undirected graph $G$, let ${\hat{I}}^3(G)$ denote the size of a smallest dominating set of $G$ and $\hat{I}¼(G)$ denote the number of eigenvalues of the Laplacian matrix of $G…