Michael Fraboni
Department of Mathematics and Computer Science
Moravian College 


The Birank Number of 3 × n Grid Graphs
with Shane Harder. Appears in The Mathematics Exchange 11.1 (2017), pp. 1–13
The Birank Number of Operationally Constructed Graphs
with Andrew Benson. To appear in Congr. Numer. 2017
The birank number of ladder, prism and Möbius ladder graphs
with Madison Zebrine while she was a student here at Moravian College.  Appears in the Australasian journal of Combinatorics, Volume 63(1) (2015), 34–40.
The birank number of a graph
with Michael Fisher at WCUPA and Darren Narayan at Rochester Institute of Technology in Congr. Numer. 204 (2010), 173-180.
Maximum graphs with unique minimum dominating set of size two
with Nathan Shank here at Moravian College in the Australasian journal of CombinatoricsVolume 46 (2010), 91–99.
Strong q-Convexity in Uniform Neighborhoods of Subvarieties in Coverings of Complex Spaces
a joint paper with Terrence Napier from Lehigh University which appeard in Mathematische Zeitschrift volume 265 (2010), no. 3, 653-685.
Fractals in the Classroom
a joint paper with Trisha Moller in Mathematics Teacher, volume 102, no. 3 (October 2008).
Culture Points: Engaging students outside the classroom
a joint paper with Kevin Hartshorn from Moravian College which appeared in PRiMUS, Volume XVII(2) (2007), pages 117-124.
q-Convexity Properties of Coverings of Complex Manifolds
appeared in Mathematische Zeitschrift, Volume 254 (2006), no. 3, 553-566
Conjugacy and the 3x+1 Conjecture
My paper about the 3x+1 problem (also known as the Collatz Conjecture). It was written as an undergraduate research project at the University of Scranton with Ken Monks.

Student Work

Upper Bounds on the Birank Number of G3,n by Shane Harder
Shane completed his honors project in the spring of 2016.
Birank Number of Operationally Constructed Graphs by Andrew Benson
Andrew completed this honors project in the spring of 2013.
The Collatz Conjecture: A Conjugacy Approach by James T Long III
I advised Jamie in his honors project which he completed in December of 2008. In addition, he presented a chapter of his thesis at the 2008 Midstates Conference on Undergraduate Research in Mathematics and Computer Science where it is published in the conference proceedings.
Explorations of the Collatz Conjecture by Kelly Latourette
I advised Kelly in her honors project which she completed in December of 2007.