Results 231 to 240 of about 59,758 (255)

The Maximum Genus of Cartesian Products of Graphs

Canadian Journal of Mathematics, 1974
The maximum genus γM(G) of a connected graph G has been defined in [2] as the maximum g for which there exists an embedding h : G —> S(g), where S(g) is a compact orientable 2-manifold of genus g, such that each one of the connected components of S(g) — h(G) is homeomorphic to an open disk; such an embedding is called cellular.
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Genus of cartesian products of regular bipartite graphs

Journal of Graph Theory, 1980
AbstractLet G(n, d) denote a connected regular bipartite graph on 2n vertices and of degree d. It is proved that any Cartesian product G(n, d) × G1(n1, d1) × G2(n2, d2) × ⃛ × Gm(nm, dm), such that max {d1, d2,…, dm} ≤ d ≤ d1 + d2 + ⃛ + dm, has a quadrilateral embedding, thereby establishing its genus, and thereby generalizing a result of White. It is
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1‐Factorizations of cartesian products of regular graphs

Journal of Graph Theory, 1979
AbstractLet G1, G2…, Gn be regular graphs and H be the Cartesian product of these graphs (H = G1 × G2 × … × Gn). The following will be proved: If the set {G1, G2…, Gn} has at leat one of the following properties: (*) for at leat one i ϵ {1, 2,…, n}, there exists a 1‐factorization of Gi or (**) there exists at least two numbers i and j such that 1 ≤ i ...
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Nonorientable genus of cartesian products of regular graphs

Journal of Graph Theory, 1982
AbstractA special type of surgery developed by A. T. White and later used by the author to construct orientable quadrilateral embeddings of Cartesian products of graphs is here expanded to cover the nonorientable case as well. This enables the nonorientable genus of many families of Cartesian products of triangle‐free graphs to be computed.
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Haplotype-resolved de novo assembly using phased assembly graphs with hifiasm

Nature Methods, 2021
Haoyu Cheng, Gregory T Concepcion, Xiaowen Feng   +2 more
exaly  

Knowledge Graphs

ACM Computing Surveys, 2022
Aidan Hogan, Claudio Gutierrez, Sabrina Kirrane   +2 more
exaly  

Physics-Inspired Structural Representations for Molecules and Materials

Chemical Reviews, 2021
Félix Musil, Andrea Grisafi, Albert P Bartók   +2 more
exaly  

Foundation models for generalist medical artificial intelligence

Nature, 2023
, Harlan M Krumholz, Jure Leskovec
exaly  

Reverse Zagreb indices of cartesian product of graphs

2015
In this paper, some exact expressions for the reverse Zagreb indices of Cartesian product of two simple connected graphs are determined. We apply our results to compute the reverse Zagreb indices of arbitrary C-4 tube and C-4 torus.
Ediz, Süleyman, Cancan, Murat
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Differential abundance testing on single-cell data using k-nearest neighbor graphs

Nature Biotechnology, 2021
Emma Dann, Neil C Henderson, Sarah A Teichmann   +2 more
exaly