Graph properties for splitting with grounded Laplacian matrices (Q1314635)

The Laplacian matrix \(L(G)\) is associated with any undirected connected graph \(G\) containing no self-loops. When solving the linear system involved one of the vertices is grounded, so the coefficient matrix is a principal submatrix of \(L\), which is called the grounded Laplacian matrix \(L_ 1\). In this paper iterative solutions of such linear systems are considered. Certain regular splittings of \(L_ 1\) are used, and an upper bound for the spectral radius of the iteration matrix in terms of the properties of the graph \(G\) is derived.