Results 1 to 10 of about 8,370 (109)
Steiner distance matrix of caterpillar graphs
Special Matrices, 2022 Abstract In this article, we show that the rank of the 2-Steiner distance matrix of a caterpillar graph having N N vertices and
Shivani Goel, Ali Azimi
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A generalization of the Graham-Pollak tree theorem to Steiner distance
Discrete MathematicsGraham and Pollak showed that the determinant of the distance matrix of a tree $T$ depends only on the number of vertices of $T$. Graphical distance, a function of pairs of vertices, can be generalized to ``Steiner distance'' of sets $S$ of vertices of arbitrary size, by defining it to be the fewest edges in any connected subgraph containing all of $S$.
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Steiner distance stable graphs
Discrete Mathematics, 1994 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.
Wayne Goddard +2 more
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Steiner Distance in Product Networks
Discrete Mathematics & Theoretical Computer Science, 2018 For a connected graph $G$ of order at least $2$ and $S\subseteq V(G)$, the \emph{Steiner distance} $d_G(S)$ among the vertices of $S$ is the minimum size among all connected subgraphs whose vertex sets contain $S$. Let $n$ and $k$ be two integers with $2\leq k\leq n$.
Yaping Mao +2 more
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Steiner symmetrals and their distance from a ball [PDF]
Israel Journal of Mathematics, 2003 For \(\varepsilon> 0\), let \(N(n,\varepsilon)\) be the minimum number of successive Steiner symmetrizations sufficient to transform any convex body in \(\mathbb{R}^n\), with volume equal to the volume of the unit ball \(B^n\), into a convex body whose Hausdorff distance from \(B^n\) is at most \(\varepsilon\).
BIANCHI, GABRIELE, GRONCHI, PAOLO
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Steiner distance and convexity in graphs
European Journal of Combinatorics, 2008 We use the Steiner distance to define a convexity in the vertex set of a graph, which has a nice behavior in the well-known class of HHD-free graphs. For this graph class, we prove that any Steiner tree of a vertex set is included into the geodesical convex hull of the set, which extends the well-known fact that the Euclidean convex hull contains at ...
José Cáceres +2 more
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Steiner intervals and Steiner geodetic numbers in distance-hereditary graphs
Discrete Mathematics, 2007 The closure of a set \(S\) of vertices in a connected graph \(G\) is \(\bigcup_{u,v\in S}I[u,v]\) where the interval \(I[u,v]\) is the union of all vertices that belong to some shortest \(u\)-\(v\) path. If the closure is \(V(G)\), then \(S\) is called a geodetic set.
Ortrud R. Oellermann, María Luz Puertas
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Extremal values for Steiner distances and the Steiner $k$-Wiener index
, 2023 Various questions related to distances between vertices of simple, finite graphs are of interest to extremal graph theorists. The Steiner distance of a set of $k$ vertices is a natural generalization of the regular distance. We extend several theorems on the middle parts and extremal values of trees from their regular distance variants to their Steiner
Wang, Hua, Zhang, Andrew
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Geodetic and Steiner geodetic sets in 3-Steiner distance hereditary graphs
Discrete Mathematics, 2008 In a connected graph \(G=(V,E)\), a set \(S\subset V\) is a (Steiner) geodetic set if all \(v\in V\) lie on some shortest path between two vertices in \(S\) (resp. some Steiner subtree for \(S\) in \(G\)). The minimum cardinality of a (Steiner) geodetic set is the (Steiner) geodetic number \(g(G)\) (resp. \(sg(G)\)).
Linda Eroh, Ortrud R. Oellermann
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On the average Steiner distance of graphs with prescribed properties
Discrete Applied Mathematics, 1997 The Steiner distance of a set \(S\) of vertices in a connected graph \(G\), \(d_G(S)\), is the number of edges in a smallest Steiner tree for \(S\). The average Steiner distance \(\mu _n(G)\) of \(G\) is the average of the Steiner distances of all \(n\)-subsets of \(V(G)\).
Peter Dankelmann +2 more
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