Perl NEARLY PERFECT SETS IN PRODUCTS OF GRAPHS
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چکیده
The study of nearly perfect sets in graphs was initiated in [2]. Let S ⊆ V (G). We say that S is a nearly perfect set (or is nearly perfect) in G if every vertex in V (G)−S is adjacent to at most one vertex in S. A nearly perfect set S in G is called maximal if for every vertex u ∈ V (G) − S, S ∪ {u} is not nearly perfect in G. The minimum cardinality of a maximal nearly perfect set is denoted by np(G). It is our purpose in this paper to determine maximal nearly perfect sets in two well-known products of two graphs, i.e. in the Cartesian product and in the strong product. Lastly, we give upper bounds of np(G1 ×G2) and np(G1 ⊗ G2), for some special graphs G1, G2.
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تاریخ انتشار 2004