Algebraic invariants arising from the chromatic polynomials of theta graphs
Citation
Export citationDelbourgo, D., & Morgan, K. (2014). Algebraic invariants arising from the chromatic polynomials of theta graphs. Australasian Journal of Combinatorics, 59(2), 293–310.
Permanent Research Commons link: https://hdl.handle.net/10289/11937
Abstract
This paper investigates some algebraic properties of the chromatic polynomials of theta graphs, i.e. graphs which have three internally disjoint paths sharing the same two distinct end vertices. We give a complete description of the Galois group, discriminant and ramification indices for the chromatic polynomials of theta graphs with three consecutive path lengths. We then do the same for theta graphs with three paths of the same length, by comparing them algebraically to the first family. This algebraic link extends naturally to generalised theta graphs with k + 1 branches.
Date
2014Type
Publisher
CMSA (Inc.)
Rights
This article is published in the Australasian Journal of Combinatorics. Used with permission.