Thursday, Feb. 16, 1:45 pm, 368 Little


Title:
Enumeration of Weighted Graphs

Speaker:         Hyeong-Kwan Ju (Chonnam National University)

Abstract:  Let G be a simple graph, n a given nonnegative integer and [n]={0, 1,
2, ... , n}. For each vertex in G we give an integer in [n] so that any sum of
two integers corresponding adjacent vertices is bounded by n. We call such a
simple graph with integers an weighted graph.

In this talk we investigate the number of weghted graphs for each specific type
of simple graphs (say, linear, circular, complete, complete bipartite, discrete,
star graphs and some of platonic graphs) and their corresponding generating
functions.

We also consider the relationship between our resulting generating functions and
certain shape of rational polytopes.

Finally, we list open problems relevant to weighted graphs.