DMG Seminar by Dr Kerri Morgan

Wed, 06 May 2026 10:00:00 +0000

Title: Why I Love Theta Graphs.

By: Dr Kerri Morgan, School of Science, RMIT.

Abstract: There are many interesting graphs. Cayley graphs have beautiful symmetries and connections with groups. The Petersen Graph has proved to be a counterexample for several past conjectures. However, my favourite graphs are Theta Graphs.

A Theta Graph consists of two distinct vertices joined by multiple internally vertex-disjoint paths.

In this talk, I present some cases where Theta Graphs (and some of their close relatives) have proved useful in the context of the chromatic polynomial. The chromatic polynomial of a graph G gives the number of proper vertex colouring of a graph. The roots of the chromatic polynomial have been extensively studied and have applications in statistical mechanics because of the relationship between the chromatic polynomial and the Potts model partition function.

The roots of the chromatic polynomial are algebraic integers. Cameron, et. al conjectured that if α was a chromatic root, there exists a natural number n such that α + n is a chromatic root. If this conjecture holds, an interesting question is what is the relationship (if any) between a graph with chromatic root α and a graph with chromatic root α + n? More generally, is there a connection between the structural properties of the graphs and the algebraic properties of the chromatic polynomials of the graphs. Theta graphs provide some insights into this question.

Bio: Kerri Morgan is a Senior Lecturer in mathematics at RMIT University, specialising in combinatorics and discrete mathematics. Her research interests include graph theory and its applications, and the connections between structural properties of networks and the algebraic properties of the related graph polynomials

Kerri Morgan | DMG

DMG Seminar by Dr Kerri Morgan