Abstract
UDC 519.1 In 2002, Gary Chartrand and Ping Zhang [<em>The Steiner number of a graph,</em> Discrete Math., <strong>242</strong>, 41--54 (2002)] characterized the connected graphs G of order p ≥ 3 with Steiner number p , p - 1 , or 2. In our paper, we characterize all connected graphs G of order p ≥ 4 with Steiner number s ( G ) = p - 2 . In addition, we obtain some sharp Nordhaus–Gaddum bounds for the Steiner number of connected graphs whose complement is also connected.
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