6 papers
Small -kernels in digraphs with minimum in-degree
Geoffrey Boyer, Matt Burnham, Daniela Černá +5
For a digraph , a subset is called a -kernel if is an independent set and all vertices in are reachable from via a directed path of length at…
Schuttes property for sets of tournaments and an application to dice games
Joel Jeffries
A tournament has Schuttes property if for every set of vertices, there is a vertex which dominates the set. In 1963, Erdos provided bounds for , the smallest order…
Enumerating Prime Patterns in Juggling Variations
Steve Butler, Vera Choi, Joel Jeffries +3
Juggling patterns can be mathematically modeled as closed walks within directed state graphs. In this paper, we present a unified framework of unbounded juggling patterns and its v…
On the Edge Derivative of the Normalized Laplacian with Applications to Kemeny's Constant
Connor Albright, Kimberly P. Hadaway, Ari Holcombe Pomerance +3
In a connected graph, Kemeny's constant gives the expected time of a random walk from an arbitrary vertex to reach a randomly-chosen vertex . Because of this, Kemeny's const…
Spectral faux trees
Steve Butler, Elena D'Avanzo, Rachel Heikkinen +3
A spectral faux tree with respect to a given matrix is a graph which is not a tree but is cospectral with a tree for the given matrix. We consider the existence of spectral faux tr…
Complements of coalescing sets
Steve Butler, Elena D'Avanzo, Rachel Heikkinen +3
We consider matrices of the form , with being the diagonal matrix of degrees, being the adjacency matrix, and a fixed value. Given a graph and $B\subseteq V(G…