On $$\alpha $$-Excellent Graphs
Magda Dettlaff, Michael A. Henning, Jerzy Topp · Bulletin of the Malaysian Mathematical Sciences Society · 2023
Abstract A graph G is $$\alpha $$ α -excellent if every vertex of G is contained in some maximum independent set of G. In this paper, we characterize $$\alpha $$ α -excellent bipartite graphs, $$\alpha $$ α -excellent unicyclic graphs, $$\alpha $$ α -excellent simplicial graphs, $$\alpha $$ α -excellent chordal graphs, $$\alpha $$ α -excellent block graphs, and we show that every generalized Petersen graph is $$\alpha $$ α -excellent.