Isometric embeddings of subdivided wheels in hypercubes

Isometric 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...

Applications of isometric embeddings to chemical graphs

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...

Isometric embeddings of subdivided complete graphs in the hypercube

Wirelength of 1-fault hamiltonian graphs into wheels and fans

In this paper we obtain a fundamental result to find the exact wirelength of 1-fault hamiltonian graphs into wheels and fans. Using this result we compute the exact wirelength of circulant graphs, generalized petersen graphs, augmented cubes, crossed cubes, mőbius cubes, locally twisted cubes, twisted cubes, twisted n-cubes, generalized twisted cubes, hierarchical cubic networks, alternating gr...

Subdivided graphs as isometric subgraphs of Hamming graphs

Résumé It is proven that given G a subdivision of a clique Kn (n ≥ 1), G is isometrically embeddable in a Hamming graph if and only if G is a partial cube or G = Kn. The characterization for subdivided wheels is also obtained.