39 citations · 123 across the 33 of their papers we have counts for
33 papers · 1 filter
Maximal Intervals of Decrease and Inflection Points for Node Reliability
Jason Brown
The \textit{node reliability} of a graph is the probability that at least one node is operational and that the operational nodes can all communicate in the subgraph that they i…
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…