QUANTUM HITTING TIME ON THE COMPLETE GRAPH

Graph embedding using a quasi-quantum analogue of the hitting times of continuous time quantum walks

In this paper, we explore analytically and experimentally a quasi-quantum analogue of the hitting time of the continuous-time quantum walk on a graph. For the classical random walk, the hitting time has been shown to be robust to errors in edge weight structure and to lead to spectral clustering algorithms with improved performance. Our analysis shows that the quasi-quantum analogue of the hitt...

Nim On The Complete Graph

The two-player game of Nim on graphs is played on a regular graph with positively weighted edges by moving alternately from a fixed starting vertex to an adjacent vertex, decreasing the weight of the incident edge to a strictly smaller non-negative integer. The game ends when a player is unable to move since all edges incident with the vertex from which the player is to move have weight zero. I...

Explicit Bound on Cover Time and Cover Time of Random Walk on Complete Bipartite Graph

Layered Percolation on the Complete Graph

We present a generalized (multitype) version of percolation on the complete graph, in which we divide the vertices of the graph into a fixed number of sets (called layers) and perform percolation where the probability of {u, v} being in our edge set depends on the respective layers of u and v. Many results analogous to usual percolation on the complete graph are determined. In addition, we dete...

On Subgraphs of the Complete Bipartite Graph

G(n) denotes a graph of n vertices and G(n) denotes its complementary graph. In a complete graph every two distinct vertices are joined by an edge. Let C k (G(n)) denote the number of complete subgraphs of k vertices contained in G(n). Recently it was proved [1] that for every k 2 (n) (1) min C (G (n)) + Ck(G(n)) < k k, , ! 2 2 where the minimum is over all graphs G(n). It seems likely that (1)...