Nonhomogeneous parking functions and noncrossing partitions.
In this paper we prove that random d-regular graphs with d ≥ 3 have traffic congestion of the order O(n logd−13 n) where n is the number of nodes and geodesic routing is used. We also show that these graphs are not asymptotically δ-hyperbolic for any non-negative δ almost surely as n → ∞.
We show using non-intersecting paths, that a random rhombus tiling of a hexagon, or a boxed planar partition, is described by a determinantal point process given by an extended Hahn kernel.
This paper determines all nonsingular unicyclic mixed graphs on at least nine vertices with at most three Laplacian eigenvalues greater than two.
The cyclicity index of a matrix is the cyclicity index of its critical subgraph, namely, the subgraph of the adjacency graph which consists of all cycles of the maximal average weight. The cyclicity index of a graph is the least common multiple of the cyclicity indices of all its maximal strongly connected subgraphs, and the cyclicity index of a strongly connected graph is the least common divisor of the lengths of its (directed) cycles. In this paper we obtain the characterization of linear, possibly...
Nordhaus-Gaddum results for weakly convex domination number of a graph G are studied.