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tK\(_p\)-saturated graphs of minimum size. (English) Zbl 1229.05141

Summary: A graph \(G\) is \(H\)-saturated if \(G\) does not contain \(H\) as a subgraph but for any nonadjacent vertices \(u\) and \(v, G+uv\) contains \(H\) as a subgraph. The parameter \(sat(H,n)\) is the minimum number of edges in an \(H\)-saturated graph of order \(n\). In this paper, we determine \(sat(H,n)\) for sufficiently large \(n\) when \(H\) is a union of cliques of the same order, an arbitrary union of two cliques and a generalized friendship graph.

MSC:

05C35 Extremal problems in graph theory
05C76 Graph operations (line graphs, products, etc.)
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References:

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