Graph-indexed random walks (or equivalently M -Lipschitz mappings of graphs) are a generalization of standard random walk on Z. For M ∈ N, an M-Lipschitz mapping of a connected rooted graph G = (V,E) is a mapping f : V → Z such that root is mapped to zero and for every edge (u, v) ∈ E we have |f(u) − f(v)| ≤ M . We study two natural problems regarding graph-indexed random walks. 1. Computing th...

In a rooted graph, a vertex is designated as its root. An outerplanar graph is represented by a plane embedding such that all vertices appear along its outer boundary. Two different plane embeddings of a rooted outerplanar graphs are called symmetric copies. Given integers n ≥ 3 and g ≥ 3, we give an O(n)-space and O(1)-time delay algorithm that enumerates all biconnected rooted outerplanar gra...

A tree T of order n is called k-placement if there are k edge-disjoint copies of T into K_{n}. In this paper we prove some results about 4-placement of rooted trees.