Graphs with large Steiner number
DOI:
https://doi.org/10.3842/umzh.v76i5.7409Keywords:
Steiner distance, Steiner set, Steiner numberAbstract
UDC 519.1
In 2002, Gary Chartrand and Ping Zhang [The Steiner number of a graph, Discrete Math., 242, 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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