Isometric embeddings of graphs
نویسندگان
چکیده
منابع مشابه
On Isometric Embeddings of Graphs
If G is a finite connected graph with vertex set V and edge set E, a standard way of defining a distance da on G is to define dG(x, y) to be the number of edges in a shortest path joining x and y in V. If (M, dM) is an arbitrary metric space, then an embedding X: V-> M is said to be isometric if dG(x, y) = dM(\(x), X(y)) for all x, y e V. In this paper we will lay the foundation for a theory of...
متن کاملIsometric embeddings in Hamming graphs
The results presented in this paper are parts of my doctoral thesis [ 193; the algorithm and some of the characterizations in Section 7 have been introduced in [ 181. Motivation for isometric embeddings into Hamming graphs has come from communication theory (Graham and Pollak [ 121) an-d linguistics (Firsov 1181). Isometric subgraphs of Hamming graphs also appear in biology as “quasi-species” (...
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Abstract. Applications of isometric embeddings of benzenoid graphs are surveyed. Their embeddings into hypercubes provide methods for computing the Wiener index and the Szeged index, while embeddings into the Cartesian product of trees lead to fast algorithms. A new method for computing the hyperWiener index of partial cubes in general, and of benzenoid graphs and trees in particular, is also p...
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Let V be an n-dimensional vector space (4 ≤ n < ∞) and let Gk(V ) be the Grassmannian formed by all k-dimensional subspaces of V . The corresponding Grassmann graph will be denoted by Γk(V ). We describe all isometric embeddings of Johnson graphs J (l,m), 1 < m < l − 1 in Γk(V ), 1 < k < n − 1 (Theorem 4). As a consequence, we get the following: the image of every isometric embedding of J (n, k...
متن کاملIsometric embeddings of subdivided connected graphs into hypercubes
Isometric subgraphs of hypercubes are known as partial cubes. These graphs have first been investigated by Graham and Pollack [R.L. Graham, H. Pollack, On the addressing problem for loop switching, Bell System Technol. J. 50 (1971) 2495–2519; and D. Djoković, Distance preserving subgraphs of hypercubes, J. Combin. Theory Ser. B 14 (1973) 263–267]. Several papers followed with various characteri...
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 1984
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.81.22.7259