John Estes, Ph.D
Professor of Mathematics, Dean of Science and Mathematics
Belhaven University
Estes is a graph theorist with a background in independence, including independence polynomials, backbone colorings, maximal outerplanar graphs, and a generalization of trees known as k-trees. In particular, he has investigated extremal cases of k-trees with regard to many metrics, including Zagreb indices. More recently, he and his students have investigated random walks through Markov chains on graphs, in particular, random walks with absorbing states. He is also interested in investigating machine learning and artificial intelligence, looking at algorithmic graph searches and supervised learning techniques.
Discipline: Mathematics
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Philip Kains, Ph.D.
Assistant Professor of Mathematics
Belhaven University
Dr. Kains is interested primarily in connectivity of graphs. The intersection of longest cycles in k-connected graphs has been studied extensively, with results having significant implications in cybersecurity. Dr. Kains’ research explores results of long cycles in k-connected graphs that are not necessarily longest in the graph overall. He is interested in path analogues for these problems as well. Additionally, Dr. Kains is interested in scheduling problems, discrete math games, and statistical modeling. He is currently working on a predictive model for baseball results and is exploring the use of machine learning in brute force solutions for graph theory.
Discipline: Mathematics
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