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Steiner Distance-Hereditary Graphs
SIAM Journal on Discrete Mathematics, 1994For a given connected graph \(G\) and a set \(S \subseteq V(G)\) the authors define the Steiner distance of \(S\) in \(G\), denoted by \(d_ G(S)\), as the smallest number of edges in a connected subgraph of \(G\) that contains \(S\). A connected graph \(G\) is \(k\)-Steiner distance-hereditary, \(k \geq 2\), if for every \(S \subseteq V(G)\) such that \
Ortrud Oellermann, Henda C Swart
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Isometric subgraphs for Steiner distance
Journal of Graph Theory, 2020AbstractLet G be a connected graph and a length‐function on the edges of G. The Steiner distance sdG(A) of A ⊆ V(G) within G is the minimum length of a connected subgraph of G containing A, where the length of a subgraph is the sum of the lengths of its edges.
Daniel Weißauer
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Semi-Distance Codes and Steiner Systems
Graphs and Combinatorics, 2007The \textit{semi-distance} between two binary vectors \(x\) and \(y\) of length \(n\) is the number of positions in which \(x\) is one and \(y\) is zero. A binary code \(C\) of length \(n\) is a \textit{\(d\)-semi-distance code} if \(C\) has minimum semi-distance \(d\).
Midori Kobayashi, Gisaku Nakamura
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MEAN STEINER DISTANCE OF VICSEK NETWORKS
Fractals, 2021The four-point Steiner distance is the minimum of the total geodesic distances within the metric space from four given points to a point. For Vicsek networks, we obtain the asymptotic formula of their mean Steiner distances using the method of finite pattern.
LEI LEI, QI JIA, BING ZHAO
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MATCH : communications in mathematical and in computer chemistry, 2017
The concept of degree distance $DD(G)$ of a connected graphs $G$ was introduced by Dobrynin and Kochetova in 1994. Recently, Gutman introduced the concept of $k$-center Steiner degree distance of a graph. The \emph{;$k$-center Steiner degree distance}; $DD_k(G)$ of a connected graph $G$ is defined by $SDD_k(G)=\sum_{;\overset{;S\subseteq V(G)};{;|S|=k};
Gutman, Ivan, Klobučar, Antoaneta
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The concept of degree distance $DD(G)$ of a connected graphs $G$ was introduced by Dobrynin and Kochetova in 1994. Recently, Gutman introduced the concept of $k$-center Steiner degree distance of a graph. The \emph{;$k$-center Steiner degree distance}; $DD_k(G)$ of a connected graph $G$ is defined by $SDD_k(G)=\sum_{;\overset{;S\subseteq V(G)};{;|S|=k};
Gutman, Ivan, Klobučar, Antoaneta
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A note on Steiner reciprocal degree distance
Discrete Mathematics, Algorithms and Applications, 2020The concept of reciprocal degree distance [Formula: see text] of a connected graph [Formula: see text] was introduced in 2012. The Steiner distance in a graph, introduced by Chartrand et al. in 1989, is a natural generalization of the concept of classical graph distance.
D. Sarala +3 more
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The average Steiner distance of a graph
Journal of Graph Theory, 1996Let \(G= (V,E)\) be a graph and let \(S\) be a subset of vertices. The Steiner distance for \(S\) is the number of edges in a smallest connected subgraph of \(G\) containing \(S\). If \(S\) consists of two vertices, the Steiner distance for \(S\) is just the distance between these vertices.
Peter Dankelmann +2 more
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ECCENTRIC STEINER DISTANCE SUM OF VICSEK NETWORKS
Fractals, 2022The topological indexes, such as the Wiener sum and the eccentric distance sum, play important roles in Chemical Graph Theory, where the eccentric distance sum characterizes the geodesic distance of two nodes. In this paper, for a family of self-similar Vicsek networks, we discuss their eccentric distance sums related to the Steiner distance of four ...
WENJIA MA, QI JIA, LEI LEI, LIFENG XI
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Distance-Hereditary Graphs, Steiner Trees, and Connected Domination
SIAM Journal on Computing, 1988Summary: Distance-hereditary graphs have been introduced by Howorka and studied in the literature with respect to their metric properties. In this paper several equivalent characterizations of these graphs are given: in terms of existence of particular kinds of vertices (isolated, leaves, twins) and in terms of properties of connections, separators ...
Marina Moscarini, Alessandro D'Atri
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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 $S$.
Gabrielle Tauscheck
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