We present an extremely fast graph drawing algorithm for very large graphs, which we term ACE (for Algebraic multigrid Computation of Eigenvectors). ACE exhibits an improvement of...
A Shilla distance-regular graph (say with valency k) is a distance-regular graph with diameter 3 such that its second largest eigenvalue equals to a3. We will show that a3 divide...
We consider a variation of the chip-firing game in a induced subgraph S of a graph G. Starting from a given chip configuration, if a vertex v has at least as many chips as its deg...
Let µ (G) and µmin (G) be the largest and smallest eigenvalues of the adjacency matrix of a graph G. Our main results are: (i) Let G be a regular graph of order n and finite di...
Let µ (G) and µmin (G) be the largest and smallest eigenvalues of the adjacency matrix of a graph G. Our main results are: (i) If H is a proper subgraph of a connected graph G o...