منابع مشابه
Steiner distance stable graphs
Let G be a connected graph and S a nonempty set of vertices of G. Then the Steiner distance d,(S) of S is the smallest number of edges in a connected subgraph of G that contains S. Let k, I, s and m be nonnegative integers with m > s > 2 and k and I not both 0. Then a connected graph G is said to be k-vertex I-edge (s,m)-Steiner distance stable, if for every set S of s vertices of G with d,(S) ...
متن کاملSteiner intervals and Steiner geodetic numbers in distance-hereditary graphs
A Steiner tree for a set S of vertices in a connected graph G is a connected subgraph of G with a smallest number of edges that contains S. The Steiner interval I (S) of S is the union of all the vertices of G that belong to some Steiner tree for S. If S = {u, v}, then I (S) = I [u, v] is called the interval between u and v and consists of all vertices that lie on some shortest u–v path in G. T...
متن کاملWiener Polynomials for Steiner Distance of Graphs
In this paper, the Wiener polynomials Wn(G;x) for some special graphs G including path graphs and cycle graphs are obtained. Moreover, for vertex-disjoint connected graphs G1 and G2, formulas for the Wiener polynomials of Steiner n-distance of compound graphs G1•G2 and G1:G2 are obtained in terms of those polynomials for G1and G2.
متن کاملThe Steiner distance dimension of graphs
For a nonempty set S of vertices of a connected graph G, the Steiner distance d(S) of S is the minimum size among all connected subgraphs whose vertex set contains S. For an ordered set W = {Wl, W2,"', Wk} of vertices in a connected graph G and a vertex v of G, the Steiner representation s(vIW) of v with respect to W is the (2k I)-vector where d i1 ,i2, ... ,ij(V) is the Steiner distance d({V,W...
متن کاملWeighted Connected Domination and Steiner Trees in Distance-Hereditary Graphs
Distance-hereditary graphs are graphs in which every two vertices have the same distance in every connected induced subgraph containing them. This paper studies distance-hereditary graphs from an algorithmic viewpoint. In particular, we present linear-time algorithms for finding a minimum weighted connected dominating set and a minimum vertex-weighted Steiner tree in a distance-hereditary graph...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2008
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2007.03.007