Results 1 to 10 of about 1,167,245 (202)
A note on the automorphism group of the Hamming graph [PDF]
Transactions on Combinatorics, 2021 Let $m>1$ be an integer and $\Omega$ be an $m$-set. The Hamming graph $H(n,m)$ has $\Omega ^{n}$ as its vertex-set, with two vertices are adjacent if and only if they differ in exactly one coordinate.
Seyed Morteza Mirafzal, Meysam Ziaee
doaj +2 more sources
PLoS Computational Biology, 2021 Graphs such as de Bruijn graphs and OLC (overlap-layout-consensus) graphs have been widely adopted for the de novo assembly of genomic short reads. This work studies another important problem in the field: how graphs can be used for high-performance ...
Yuansheng Liu, Jinyan Li
doaj +2 more sources
Tree-Like Partial Hamming Graphs
Discussiones Mathematicae Graph Theory, 2014 Tree-like partial cubes were introduced in [B. Brešar, W. Imrich, S. Klavžar, Tree-like isometric subgraphs of hypercubes, Discuss. Math. Graph Theory, 23 (2003), 227-240] as a generalization of median graphs.
Gologranc Tanja
doaj +2 more sources
Discussiones Mathematicae Graph Theory, 2016 For k ∈ ℤ+ and G a simple, connected graph, a k-radio labeling f : V (G) → ℤ+ of G requires all pairs of distinct vertices u and v to satisfy |f(u) − f(v)| ≥ k + 1 − d(u, v). We consider k-radio labelings of G when k = diam(G).
Niedzialomski Amanda
doaj +2 more sources
Hamming Distance Encoding Multihop Relation Knowledge Graph Completion
IEEE Access, 2020 Knowledge graphs (KGs) play an important role in many real-world applications like information retrieval, question answering, relation extraction, etc. To reveal implicit knowledge from a knowledge graph (KG), viz.
Panfeng Chen +4 more
doaj +2 more sources
Spectral Characterization of the Hamming Graphs [PDF]
SSRN Electronic Journal, 2007 It is shown that the Hamming graph \(H(3,q)\) with diameter three is uniquely determined by its spectrum for \(q\geq 36\). It is also demonstrated that for given integer \(D\geq 2\), any graph cospectral with the Hamming graph \(H(D,q)\) is locally the disjoint union of \(D\) copies of the complete graph of size \(q-1\), for \(q\) large enough.
Bang, S, van Dam, ER, Koolen, JH
openaire +9 more sources
On induced subgraphs of the Hamming graph [PDF]
Journal of Graph Theory, 2020 AbstractIn connection with his solution of the Sensitivity Conjecture, Hao Huang (arXiv: 1907.00847, 2019) asked the following question: Given a graph with high symmetry, what can we say about the smallest maximum degree of induced subgraphs of with vertices, where denotes the size of the largest independent set in ?
Dingding Dong
openaire +4 more sources
Semantic ECG hash similarity graph [PDF]
Scientific ReportsGraph-based methods have made significant progress in addressing the dependent correlations among ECG time series variables. However, most existing graph structures primarily focus on local similarity while overlooking global semantic correlation ...
Yixian Fang, Shilin Zhang, Yuwei Ren
doaj +2 more sources
Graphs and CombinatoricsThe Hamming graph $H(n,q)$ is defined on the vertex set $[q]^n$ and two vertices are adjacent if and only if they differ in precisely one coordinate. Alon \cite{Alon} proved that the burning number of $H(n,2)$ is $\lceil\frac n2\rceil+1$. In this note we give a short proof of a fact that the burning number of $H(n,q)$ is $(1-\frac 1q)n+O(\sqrt{n\log n})
N. Tokushige
openaire +4 more sources
Sensitivity and Hamming graphs
arXiv.orgFor any $m\geq 3$ we show that the Hamming graph $H(n,m)$ admits an imbalanced partition into $m$ sets, each inducing a subgraph of low maximum degree. This improves previous results by Tandya and by Potechin and Tsang, and disproves the Strong $m$-ary Sensitivity Conjecture of Asensio, García-Marco, and Knauer. On the other hand, we prove their weaker
Asensio, Sara +3 more
openaire +3 more sources