Title : Random Cubic Sum Graphs
Speaker : Andrew Beveridge
When : 4:30-5:30pm April 19
Where : PPB 300
Abstract:
Consider set of all graphs whose nodes are labeled with non-identity elements of the n-dimensional hypercube so that there is an edge between nodes with labels $a$ and $b$ if and only if the node $a+b$ is also in the graph (where $a+b$ is the group operation).
A random cubic sum graph is a randomly chosen element from this set where each vertex is included independently with probability $p$. As $p$ increases from $0$ to $1$, the expected structure undergoes radical changes. As with classical random graphs, we obtain thresholds functions for graph properties. In this talk, we characterize the threshold for the appearance of the first triangle, the threshold for isolated triangles and the threshold for connectivity.
