Inverse Problem on the Steiner Wiener Index
The Wiener index ) of a connected graph , introduced by Wiener in 1947, is defined as ) =∑ ), where ) is the distance (the length a shortest path) between the vertices and in . For ⊆ ( ), the ) of the vertices of , introduced by Chartrand . in 1989, is the minimum size of a connected subgraph of who...
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| Veröffentlicht in: | Discussiones Mathematicae. Graph Theory 2018-01, Vol.38 (1), p.83-95 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | The Wiener index
) of a connected graph
, introduced by Wiener in 1947, is defined as
) =∑
), where
) is the distance (the length a shortest path) between the vertices
and
in
. For
⊆
(
), the
) of the vertices of
, introduced by Chartrand
. in 1989, is the minimum size of a connected subgraph of
whose vertex set contains
. The
) of
is defined as
. We investigate the following problem: Fixed a positive integer
, for what kind of positive integer
does there exist a connected graph
(or a tree
) of order
≥
such that
) =
(or
) =
)? In this paper, we give some solutions to this problem. |
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| ISSN: | 1234-3099 2083-5892 |
| DOI: | 10.7151/dmgt.2000 |