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Steiner distance stable graphs. (English) Zbl 0809.05042

The authors give a short overview of useful notions and results dealing with Steiner distance stable graphs. They generalize these notions and define \(k\)-vertex \(l\)-edge \((s,m)\)-Steiner distance stable graphs, where \(k\), \(l\), \(s\) and \(m\) are nonnegative integers with \(m\geq s\geq 2\) and \(k\) and \(l\) are not both zero. The authors study relatively hard mathematical problems and also discuss the computational complexity of some of them.

MSC:

05C12 Distance in graphs
05C85 Graph algorithms (graph-theoretic aspects)
68Q25 Analysis of algorithms and problem complexity
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References:

[1] Ali, H. H.; Boals, A.; Sherwani, N. S., Distance stable graphs, 2nd Internat. Conf. in Graph Theory, Combinatorics, Algorithms and Applications (1989), San Francisco
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