39 citations · 123 across the 33 of their papers we have counts for
7 papers · 1 filter
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…
Acyclic polynomials of graphs
Caroline Barton, Jason I. Brown, David A. Pike
For each nonnegative integer , let be the number of -subsets of that induce an acyclic subgraph of a given graph . We define $A(G,x) = \sum_{i \geq 0} a_i x^i…
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…
Extension to the Beraha-Kahane-Weiss Theorem with Applications
Jason Brown, Peter T. Otto
The beautiful Beraha-Kahane-Weiss theorem has found many applications within graph theory, allowing for the determination of the limits of root of graph polynomials in settings as…
Roots of Two-Terminal Reliability
Jason Brown, Corey D. C. DeGagne
Assume that the vertices of a graph are always operational, but the edges of are operational independently with probability . For fixed vertices and , th…