منابع مشابه
On Distance Preserving and Sequentially Distance Preserving Graphs
A graph H is an isometric subgraph of G if dH(u, v) = dG(u, v), for every pair u, v ∈ V (H). A graph is distance preserving if it has an isometric subgraph of every possible order. A graph is sequentially distance preserving if its vertices can be ordered such that deleting the first i vertices results in an isometric subgraph, for all i ≥ 1. We give an equivalent condition to sequentially dist...
متن کاملOn Constructing Regular Distance-Preserving Graphs
Let G be a simple, connected graph on n vertices. Let dG(u, v) denote the distance between vertices u and v in G. A subgraph H of G is isometric if dH(u, v) = dG(u, v) for every u, v ∈ V (H). We say that G is a distancepreserving graph if G contains at least one isometric subgraph of order k for every k, 1 ≤ k ≤ n. In this paper we construct regular distance-preserving graphs of all possible or...
متن کاملOn the distance preserving trees in graphs
For a vertex v of a graph G, a spanning tree T of G is distancepreserving from v if, for any vertex w, the distance from v to w on T is the same as the distance from v to w on G. If two vertices u and v are distinct, then two distance-preserving spanning trees Tu from u and Tv from v are distinct in general. A purpose of this paper is to give a characterization for a given weighted graph G to h...
متن کاملDistance preserving graphs and graph products
If G is a graph then a subgraph H is isometric if, for every pair of vertices u, v of H, we have dH(u, v) = dG(u, v) where d is the distance function. We say a graph G is distance preserving (dp) if it has an isometric subgraph of every possible order up to the order of G. We give a necessary and sufficient condition for the lexicographic product of two graphs to be a dp graph. A graph G is seq...
متن کاملDistance-Preserving Subgraphs of Interval Graphs
We consider the problem of finding small distance-preserving subgraphs of undirected, unweighted interval graphs with k terminal vertices. We prove the following results. 1. Finding an optimal distance-preserving subgraph is NP-hard for general graphs. 2. Every interval graph admits a subgraph with O(k) branching vertices that approximates pairwise terminal distances up to an additive term of +...
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ژورنال
عنوان ژورنال: Combinatorics, Probability and Computing
سال: 2012
ISSN: 0963-5483,1469-2163
DOI: 10.1017/s096354831200003x