Department of Mathematics, University of Kuwait
ABSTRACT
A T-graph is a graph with two disjoint maximal stable sets. The notions r-T-graph and
edge-T-graph are introduced, the implications
2-T-graph + edge-T-graph -+ 1-T-graph + T-graph
are true but the converse of each is false.
The main result is that if in a graph G, 2 < deg (V) < 3 for every vertex n, then G is a 2-T-graph.
We follow the terminology of Berge (1973). A graph is called a T-graph if it has two disjoint maximal stable sets.