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Cut Vertices and Isolated Vertices in Zero-Divisor Graphs

 Dr. Shane Redmond
Dr. Shane Redmond / Eastern Kentucky University
Over the last twenty years, mathematicians have begun various ways of using graphs to understand abstract algebraic systems.  One of these, the zero-divisor graph, can be used to study rings.  The goals of the theory of zero-divisor graphs are to determine which features will appear in the graph of a ring and to determine which algebraic properties of a ring are revealed from its graph.  In this talk, we will review the basic results in the study of zero-divisor graphs and completely determine when these graphs have cut vertices or isolated vertices.  (The ideas in this talk should be accessible to any student with more than one semester of abstract algebra.)
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