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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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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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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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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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The Steiner distance dimension of graphs [PDF]
Australas. J Comb., 1999 For a connected graph the authors define the Steiner basis and the Steiner distance dimension. These notions have a close relation to some chemical problems. The authors then describe graphs with \(n\) vertices that have (i) Steiner dimension 1 or \(n-1\) and (ii) Steiner dimension \(n-2\) for \(n\geq 4\).
Michael E. Raines, Ping Zhang 0004
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On Steiner minimal trees withL p distance
Algorithmica, 1992Let \(L\) be the plane with the distance \(d_ p((x_ 1,x_ 2),(y_ 1,y_ 2))=(| x_ 1-x_ 2|^ p+| y_ 1-y_ 2|^ p)^{1/p}\). Let \(P\) be a finite set of points in \(L_ p\) and let \(L_ s(P)\) be the length of a Steiner minimal tree, i.e. of a shortest network interconnecting \(P\) which may contain vertices not in \(P\) --- called Steiner points.
Zicheng Liu 0001, Ding-Zhu Du
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The 2-Steiner distance matrix of a tree
Linear Algebra and its Applications, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Azimi, Ali +1 more
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On Steiner Minimal Trees with Rectilinear Distance
SIAM Journal on Applied Mathematics, 1976We consider Steiner minimal trees in the plane with rectilinear distance. The rectilinear distance $d(p_1 ,p_2 )$ between two points $p_1 $, $p_2 $ is $| {x_1 - x_2 } | + | {y_1 - y_2 } |$, where the $(x_i ,y_i )$ are the Cartesian coordinates of the $p_i $. For a given finite set P of points, let $l_s $ denote the length of a Steiner minimal tree and $
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Steiner Distance Polynomial of Graph
مجلة الباحث الجامعي للعلوم الانسانية, 2006يتم تعريف متعدد الحدود لمسافة n-شتاينر للرسم البياني المتصل G, Wn(G;x)، على أنه Mn(G,k)xkm حيث Mn(G, k) هو عدد مجموعات n من رؤوس G التي تكون على مسافة-n K. يتم الحصول على Wn(G;x) لبعض الرسوم البيانية الخاصة وللرسم البياني المركب G1 • G2 وG1:G2. علاوة على ذلك، فإننا نعطي حدًا أعلى لمتوسط المسافة n μn(G)
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Path-distance heuristics for the Steiner problem in undirected networks
Algorithmica, 1992The authors give a common characterization of three heuristics for the Steiner minimum tree problem: shortest path heuristic, distance network heuristic and average distance heuristic. The foregoing single path heuristics and some variations are extended using repetitive application of the shortest path heuristic.
Winter, P., Smith, J.M.
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