39 citations · 123 across the 33 of their papers we have counts for
6 papers · 1 filter
Maximum Modulus of Independence Roots of Graphs and Trees
Jason I. Brown, Ben Cameron
The independence polynomial of a graph is the generating polynomial for the number of independent sets of each size and its roots are called independence roots. We bound the maximu…
On the roots of the subtree polynomial
Jason I. Brown, Lucas Mol
For a tree , the subtree polynomial of is the generating polynomial for the number of subtrees of . We show that the complex roots of the subtree polynomial are contained…
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…
On the Reliability Roots of Simplicial Complexes and Matroids
J. I. Brown, C. D. C. DeGagne
Assume that the vertices of a graph are always operational, but the edges of fail independently with probability . The \emph{all-terminal reliability} of is…
On the Stability of Independence Polynomials
Jason Brown, Ben Cameron
The independence polynomial of a graph is the generating polynomial for the number of independent sets of each size, and its roots are called {\em independence roots}. We investiga…
On the roots of Wiener polynomials of graphs
Jason I. Brown, Ortrud Oellermann, Lucas Mol
The Wiener polynomial of a connected graph is defined as , where denotes the distance between and , and the sum is taken over all unorde…