On some well covered graphs

If all maximal independent sets of a graph G have the same cardinality, then G is called a well covered graph. In this paper, we study the well covered property for several classes of graphs. We show that the line graph of a complete graphs L(Kn) is a well covered graph. Furthermore, we show that (m, n)-lollipop graph Lm,n is a well covered graph only if n = 2 and the line graph of (m, n)-lollipop graph L(Lm,n) is a well covered graph only if m is even and n = 1 or n = 3 or if m is odd and n = 2.