On Equality in an Upper Bound for the Domination Number with Respect to Nondegenerate Properties
نویسنده
چکیده
For a graph property P and a graph G , a subset S of vertices of G is a P -set if the subgraph induced by S has the property P . The domination number with respect to the property P , denoted by γP(G) , is the minimum cardinality of a dominating P -set. Any property P satisfied by all edgeless graphs is called nondegenerate. For any graph G with n vertices and maximum degree ∆(G) , γP(G) ≤ n−∆(G) where P is nondegenerate and closed under union with K1. In this paper we characterize the connected graphs and the connected triangle-free graphs which achieve this upper bound.
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