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MS (Master of Science)
Date of Award
Committee Chair or Co-Chairs
Teresa W. Haynes
Debra J. Knisley, Anant P. Godbole
Let S ⊆ V be an arbitrary subset of vertices of a graph G = (V,E). The differential ∂(S) equals the difference between the cardinality of the set of vertices not in S but adjacent to vertices in S, and the cardinality of the set S. The differential of a graph G equals the maximum differential of any subset S of V . A set S is called a zero set if ∂(S) = 0. In this thesis we introduce the study of zero sets in graphs. We give proofs of the existence of zero sets in various kinds of graphs such as even order graphs, bipartite graphs, and graphs of maximum degree 3. We also give proofs regarding the existence of graphs which contain no zero sets and the construction of zero-free graphs from graphs which contain zero sets.
Thesis - restricted
Scott, Hamilton, "Zero Sets in Graphs." (2010). Electronic Theses and Dissertations. Paper 1705. https://dc.etsu.edu/etd/1705
Copyright by the authors.