| Popis: |
The set Si,n={0,1,2,…,n−1,n}\{i}{S}_{i,n}=\left\{0,1,2,\ldots ,n-1,n\right\}\setminus \left\{i\right\}, 1⩽i⩽n1\leqslant i\leqslant n, is called Laplacian realizable if there exists an undirected simple graph whose Laplacian spectrum is Si,n{S}_{i,n}. The existence of such graphs was established by Fallat et al. (On graphs whose Laplacian matrices have distinct integer eigenvalues, J. Graph Theory 50 (2005), 162–174). In this article, we consider graphs whose Laplacian spectra have the form S{i,j}nm={0,1,2,…,m−1,m,m,m+1,…,n−1,n}\{i,j},0 |
