Min-Jen Jou

TL;DR: In this article, the problem of determining the largest number of maximum independent sets of a graph of order n is studied, and solutions to this problem are given for various classes of graphs, including general graphs, trees, forests, (connected) graphs with at most one cycle, connected graphs and triangle-free graphs.

TL;DR: This paper determines the largest number of maximal independent sets among all connected graphs of order n, which contain at most one cycle, and characterize those extremal graphs achieving this maximum value.

TL;DR: In this article, it was shown that every connected triangle, free graph of order n ⩾ 22 has at most 5 · 2 (n−6)/2 maximal independent sets if n is even (respectively, odd).

TL;DR: The setS(k) of all graphsG withmi(G) = k and without isolated vertices (exceptG ≅ K1) or duplicated vertices is studied and it is proved that |V(G)| ≤ 2k−1 +k − 2 for anyG inS(K) andk ≥ 2; consequently,S( k) is finite for anyk.