is taken over all subgraphs H for which the denominator is not zero. They also defined the strength of a graph as where the maximum is taken over all subsets S of E(G) for which the denominator is not zero. Additionally, they characterized uniformly dense graphs, and have found several classes of uniformly dense graphs and several ways of constructing such graphs. Hobbs has also done research in matroid theory. Publications Dr. Hobbs has 40 publications in graph theory, and in 1989 co-authored the book Elementary Linear Algebra. He has also written an essay on how to read research papers. A few publications are listed below: Hobbs, Arthur M.; Kannan, Lavanya; Lai, Hong-Jian; Lai, Hongyuan; Weng, Guoqing Balanced and 1-balanced graph constructions. Discrete Appl. Math. 158 (2010), no. 14, 1511–1523. Fleischner, Herbert; Hobbs, Arthur M.; Tapfuma Muzheve, Michael Hamiltonicity in vertex envelopes of plane cubic graphs. Discrete Math. 309 (2009), no. 14, 4793–4809. Kannan, Lavanya; Hobbs, Arthur; Lai, Hong-Jian; Lai, Hongyuan Transforming a graph into a 1-balanced graph. Discrete Appl. Math. 157 (2009), no. 2, 300–308 A. M. Hobbs, H.-J. Lai, H. Lai, and G. Weng, Constructing Uniformly Dense Graphs, preprint, October 1, 1994 References External links Arthur Hobbs, Texas A&M University 1940 births Living people People from Washington, D.C. University of Michigan College of Literature, Science, and the Arts alumni 20th-century American mathematicians 21st-century American mathematicians Graph theorists