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Franklin Kenter



Professor Kenter's research focuses on graph theory, broadly construed, including:

  • Spectral graph theory
  • Network science
  • Network modeling
  • Games on graphs


  1.  “Generative Markov Model for Bowling Scores”
     with Douglas Vanderwerken
     Journal of Quantitateive Analysis of Sports, in press.
  2. Proof of a conjecture of Graham and Lovász concerning unimodality of coefficients of the distance characteristic polynomial of a tree”
     with Ghodratollah Aalipour, Aida Abiad, Zhanar Berikkyzy, Leslie Hogben, Jephian C.-H. Lin and Michael Tait

     Electronic Journal of Linear Algebra, in press.
  3. “On the error of a priori sampling: zero forcing sets and propagation time”
     with Jephian C.-H. Lin
     Linear Algebra and Its Applications, in press.
  4.  “Pebbling on Graph Products and other Binary Graph Constructions”
     with John Asplund and Glenn Hurlbert
     The Australasian Journal of Combinatorics, 7-2 (2018). pp. 246-260.
  5. “The relationship between k-forcing and k-power domination”
     with Daniela Ferrero, Leslie Hogben, and Michael Young

     Discrete Mathematics, 341-6 (2018), pp 1789-1797.
  6.  “Note on power propagation time and lower bounds for the power domination number"
     with Daniela Ferrero, Leslie Hogben and Michael Young
     Journal of Combinatorial Optimization (2016).
  7.  "Interception in Distance-Vector Routing Networks"
     with David Burstein, Jeremy Kun and Feng Shi
     Journal of Complex Networks, 5-2, (June 2017), pp. 179–198.
  8.  “Iterated Prisoner's Dilemma with Extortionate Zero-Determinant Strategies and Random-Memory Opponents”
    with Emily Meigs
     Proceedings of the IEEE Congress on Evolutionary Computation 2016.
  9.  “Sharp Spectral Bounds of Several Graph Parameters using Eigenvector Norms”
     Linear Algebra and Its Applications, 504 (2016), pp. 48-63.
  10.  “On the Principal Permanent Rank Characteristic Sequences of Graphs and Digraphs”
     with Keivan Hassani Monfared, Paul Horn, Kathleen Nowak, John Sinkovic, and Josh Tobin
     Electronic Journal of Linear Algebra, 31 (2016), pp. 187-199.
  11.  “On distance spectra of graphs”
     with Ghodratollah Aalipour, Aida Abiad, Zhanar Berikkyzy, Jay Cummings, Jessica De Silva, Wei Gao, Kristin Heysse,   Leslie Hogben, Jephian C.-H. Lin, and Michael Tait
     Linear Algebra and Its Applications, 497 (2016), pp. 66-87.
  12.  “Approximating the Minimum Rank of a Graph via Alternating Projections”
     Operations Research Letters,
    44-2 (2015), pp. 255-259
  13.  “Lower Bounds on the Distance Domination Number of a Graph”
     with Randy Davila, Caleb Fast, and Michael Henning
     Contributions to Discrete Mathematics, 12-2, pp. 11-21
  14.  “Hat-Guessing Applications to the Card Game ‘Hanabi’”
     with Chris Cox, Jessica De Silva, Philip DeOrsey, Troy Retter, and Joshua Tobin
     Mathematics Magazine, 88-5 (December 2015), pp. 323-336.
  15.  “Zero Forcing on Triangle-Free Graphs”
     with Randy Davila
     Theory and Applications of Graphs, 2-2 (2015) pp. 1-8.
  16.  “An Analysis of the Basketball Endgame: When to Foul When Leading and Trailing”
     Ninth Annual MIT Sloan Sports Analytics Conference,
    published online (2015).
  17.  “A Linear Cheeger Inequality using Eigenvector Norms”
      Journal of Combinatorics,
    6-3 (2015) pp. 285-294.
  18.  “How To Win Your Betting Pool with Jensen's Inequality and the Law of Large Numbers”
      American Mathematical Monthly, 123-6 (2016), pp. 592-596
  19.  “Discrepancy Inequalities for Directed Graphs”
      with Fan Chung
      Discrete Applied Mathematics, 176 (2014), pp. 30-42.
  20.  “Necessary Spectral Conditions for Coloring Hypergraphs”
    J. Combinatorial Computing and Machine Computing, 88 (2014), pp. 73-84


  1. "Pebbling on Directed Graphs with Fixed Diameter"
    with John Asplund

Unpublished Notes:

  1. “It's good to be ϕ: a solution to a problem of Gosper and Knuth”  (2017)


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