Physical Sciences and Mathematics Commons^™

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 …