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Explorations In The Classification Of Vertices As Good Or Bad., Eugenie Marie Jackson
Explorations In The Classification Of Vertices As Good Or Bad., Eugenie Marie Jackson
Electronic Theses and Dissertations
For a graph G, a set S is a dominating set if every vertex in V-S has a neighbor in S. A vertex contained in some minimum dominating set is called good; otherwise it is bad. A graph G has g(G) good vertices and b(G) bad vertices. The relationship between the order of G and g(G) assigns the graph to one of four classes.
Our results include a method of classifying caterpillars. Further, we develop realizability conditions for a graph G given a triple of nonnegative integers …