PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Mary Anne Raymond.

Title:Enumeration of the degree sequences of non-separable graphs and connected graphs
Seminar:Combinatorics/Partitions Seminar
Speaker:Dr. James Sellers, Department of Mathematics, The Pennsylvania State University
Abstract:
In 1962, S. L. Hakimi proved necessary and sufficient conditions for a given sequence of positive integers d_1, d_2, ..., d_n to be the degree sequence of a non-separable graph or that of a connected graph. Our goal in this talk is to utilize Hakimi's results to provide generating functions for the functions d_{ns}(2m) and d_c(2m), the number of degree sequences with degree sum 2m representable by non-separable graphs and connected graphs (respectively). From these generating functions, we prove nice formulas for d_{ns}(2m) and d_c(2m) which are simple linear combinations of the values of p(j), the number of integer partitions of j. The proofs are elementary and the talk will be accessible to a wide audience. This is joint work with Oystein Rodseth and Helge Tverberg, both from the University of Bergen, Norway.

Room Reservation Information

Room Number:MB106
Date:09 / 02 / 2008
Time:11:15am - 12:05pm