Date of Award


Degree Name

Doctor of Philosophy



First Advisor

Dr. Yousef Alavi

Second Advisor

Dr. Kenneth Williams

Third Advisor

Dr. Joseph Buckley

Fourth Advisor

Dr. Kung-Wei Yang


A maximal independent set of a graph G is an independent set which is not contained properly in any other independent set of G. An independent set is called maximum if it is of largest cardinality. Denote i(G) to be the number of maximal independent sets of G. These special sets and the parameter i(G) have interested many researchers leading to a number of properties and results. One of these is the determination of the maximum number of maximal independent sets among all graphs of order n, and the external graphs. In this investigation,we develop new properties for the number of maximal independent sets i(G) and the number of maximum independent sets im(G), as well as determine the largest number of maximal and maximum independent sets possible in k-connected graph of order n(with n large) and characterize the respective external graphs. Finally, we determine the corresponding values for bipartite graphs and connected bipartite graphs, and characterize the external graphs.

Access Setting

Dissertation-Open Access