A graph G is called well covered if every two maximal independent sets of G have the same number of vertices. In this paper, we characterize well covered simplicial, chordal and circular arc graphs. © 1996 John Wiley & Sons, Inc.

In this paper, we determine upper and lower bounds for the number of independent sets in a unicyclic graph in terms of its order. This gives an upper bound for the number of independent sets in a connected graph which contains at least one cycle. We also determine the upper bound for the number of independent sets in a unicyclic graph in terms of order and girth. In each case we characterize the extremal graphs.

No abstract

No abstract

Let a and b be integers 4 ≤ a ≤ b. We give simple, sufficient conditions for graphs to contain an even [a, b]-factor. The conditions are on the order and on the minimum degree, or on the edge-connectivity of the graph.

No abstract

No abstract

Abstract. We prove that for any graph G the edge-deleted subgraphs of G partition into two isomorphism classes if and only if the edges of G partition into two orbits under the automorphism group of G.