1 citations · 2 across the 5 of their papers we have counts for
7 papers
On the Real Roots of Domination Polynomials
Iain Beaton, Jason I. Brown
A dominating set of a graph of order is a subset of the vertices of such that every vertex is either in or adjacent to a vertex of . The domination polynomia…
On the Unimodality of Domination Polynomials
Iain Beaton, Jason I. Brown
A polynomial is said to be unimodal if its coefficients are non-decreasing and then non-increasing. The domination polynomial of a graph is the generating function of the numbe…
The Average Order of Dominating Sets of a Graph
Iain Beaton, Jason I. Brown
This papers focuses on the average order of dominating sets of a graph. We find the extremal graphs for the maximum and minimum value over all graphs on vertices, while for tre…
Chromatic polynomials of 2-edge coloured graphs
I. Beaton, D. Cox, C. Duffy +1
Using the definition of colouring of -edge-coloured graphs derived from -edge-coloured graph homomorphism, we extend the definition of chromatic polynomial to -edge-colour…
Optimal Domination Polynomials
I. Beaton, J. I. Brown, D. Cox
Let be a graph on vertices and edges and the domination polynomial of . In this paper we completely characterize the values of and for which optimal…
Independence Equivalence Classes of Paths and Cycles
Iain Beaton, Jason I. Brown, Ben Cameron
The independence polynomial of a graph is the generating polynomial for the number of independent sets of each size. Two graphs are said to be \textit{independence equivalent} if t…