Chromatic and flow polynomials of generalized vertex join graphs and outerplanar graphs
Discrete Mathematics
2015-01-20 v1 Combinatorics
Abstract
A generalized vertex join of a graph is obtained by joining an arbitrary multiset of its vertices to a new vertex. We present a low-order polynomial time algorithm for finding the chromatic polynomials of generalized vertex joins of trees, and by duality we find the flow polynomials of arbitrary outerplanar graphs. We also present closed formulas for the chromatic and flow polynomials of vertex joins of cliques and cycles, otherwise known as "generalized wheel" graphs.
Cite
@article{arxiv.1501.04388,
title = {Chromatic and flow polynomials of generalized vertex join graphs and outerplanar graphs},
author = {Boris Brimkov and Illya V. Hicks},
journal= {arXiv preprint arXiv:1501.04388},
year = {2015}
}
Comments
14 pages