John T. Saccoman

Uniformly optimally reliable graphs

A graph with n nodes and e edges, where the nodes are perfectly reliable and the edges fail independently with equal probability ρ, is said to be uniformly optimally reliable (UOR) if it has the greatest reliability among all graphs with the same number of nodes and edges for all values of ρ. UOR simple graphs have been identified in the classes e = n − 1, e = n, e = n + 1, and e = n + 2 (Boesch et al., Networks21 (199) 181–194). In this paper, we demonstrate that the UOR simple graphs in these classes are also UOR when the classes are extended to include multigraphs.

Spanning tree results for graphs and multigraphs : a matrix-theoretic approach

Graph Theory Background Matrix Theory Background, including Kroenecker Products, and Proofs of the Binet - Cauchy and Courant - Fischer Theorems Spanning Tree Results for a Host of Graphs as well as Multigraphs Node-Arc Incidence Matrix Temperleys B Matrix. Multigraphs Eigenvalues and Eigenvalue Bounds A Lagrange Multiplier Approach to the Spanning Tree Problem.

The keystone combination: team teaching in a sabermetrics course

ABSTRACT The Society for American Baseball Research (SABR), formed in 1971, has given rise to the term “Sabermetrics”, which noted practitioner Bill James has defined as “the search for objective knowledge about baseball.” Mathematics, by its very nature, is objective, but baseball opinion is often based on a subjective interpretation of events. Thus, a one-credit course in Sabermetrics team-taught by two professors allows for a broader range of opinion to be introduced in class. Students also benefit from the two different teaching styles offered