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1–2–3 conjecture (11) 11
1-2-3 conjecture (8) 8
mathematics, applied (6) 6
graphs (5) 5
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6 tetrapyridine (1) 1
6-hydroxydopamine (1) 1
6-ohda: 6-hydroxydopamine (1) 1
[ info.info-dm ] computer science [cs]/discrete mathematics [cs.dm] (1) 1
[ math.math-co ] mathematics [math]/combinatorics [math.co] (1) 1
[formula omitted]-choosable graphs (1) 1
[formula omitted]-distant irregularity strength of a graph (1) 1
[formula omitted]-edge-weight choosability (1) 1
[formula omitted]-total weight choosability (1) 1
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Discrete Applied Mathematics, ISSN 0166-218X, 09/2019, Volume 268, pp. 1 - 9
The well-known 1–2–3 Conjecture asserts that the edges of every graph without isolated edges can be weighted with 1, 2 and 3 so that adjacent vertices receive distinct weighted degrees... 
Graph decomposition | 1–2–3 Conjecture | Locally irregular graph | 1-2-3 Conjecture | MATHEMATICS, APPLIED | REGULAR GRAPHS | IRREGULAR CHROMATIC INDEX | STRENGTH | Graph theory | Decomposition | Apexes | Upper bounds | Computer Science | Discrete Mathematics
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 12/2018, Volume 251, Issue 83-92, pp. 83 - 92
The 1–2–3 Conjecture asks whether every graph with no connected component isomorphic to K2 can be 3-edge-weighted so that every two adjacent vertices u and v can be distinguished via the sum of their incident... 
1–2–3 Conjecture | Difference-2 distinction | Bipartite graphs | 1-2-3 Conjecture | MATHEMATICS, APPLIED | Algorithms | Weighting | Applied mathematics | Apexes | Weights & measures | Graphs | Graph theory | Polynomials | Sums | Computer Science | Discrete Mathematics
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 09/2020, Volume 284, pp. 124 - 137
... of 4 should also be true. We verify this conjecture in this work. This work takes place in a recent “quest... 
1–2–3 Conjecture | Directed variants | Bounds | Complexity | Choosability | Computer Science | Discrete Mathematics
Journal Article
Discrete Mathematics, ISSN 0012-365X, 02/2019, Volume 342, Issue 2, pp. 498 - 504
Let G=(V,E) be any graph without isolated edges. The well known 1–2–3 Conjecture asserts that the edges of G can be weighted with 1,2,3 so that adjacent vertices have distinct weighted degrees, i.e... 
Graph decomposition | Locally irregular graph | 1–2–3 conjecture | MATHEMATICS | 1-2-3 conjecture | IRREGULAR CHROMATIC INDEX | STRENGTH | GRAPHS
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 03/2018, Volume 238, pp. 77 - 85
...-offset Hamilton cycle in the random k-uniform hypergraph Hn,p(k). We also examine this structure’s natural connection to the 1–2–3 Conjecture. 
Random hypergraphs | Group colorings | Hamilton cycles | 1–2–3 Conjecture | 1-2-3 Conjecture | MATHEMATICS, APPLIED | RANDOM GRAPHS
Journal Article
Journal of combinatorial theory. Series B, ISSN 0095-8956, 03/2020
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 12/2017, Volume 233, pp. 159 - 165
...). This graph invariant provides a natural link between the well known 1–2–3 Conjecture and irregularity strength of graphs... 
Irregularity strength of a graph | 1–2–3 Conjecture | [formula omitted]-distant irregularity strength of a graph | r-distant irregularity strength of a graph | 1-2-3 Conjecture | DENSE GRAPHS | MATHEMATICS, APPLIED | TREES | REGULAR GRAPHS | Mathematics - Combinatorics
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 04/2019, Volume 90, Issue 4, pp. 561 - 564
This paper confirms the 1‐2‐3‐conjecture for graphs that can be edge‐decomposed into cliques of order at least 3... 
edge weightings | dense graphs | 1‐2‐3‐conjecture | 1-2-3-conjecture | MATHEMATICS
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 07/2017, Volume 85, Issue 3, pp. 669 - 690
.... We prove the conjecture is valid for planar graphs of sufficiently large maximum degree. In fact an even stronger statement holds, as the necessary number of colors... 
neighbor sum distinguishing index | planar graph | adjacent strong chromatic index | 1–2–3 Conjecture | discharging method | 1-2-3 Conjecture | MATHEMATICS | IRREGULARITY STRENGTH | DISTINGUISHING EDGE COLORINGS
Journal Article
Discrete Mathematics, ISSN 0012-365X, 10/2018, Volume 341, Issue 10, pp. 2661 - 2671
...)-choosable, which implies that the 1–2–3 conjecture is true for such graphs. This improves the results in Cranston et al. (2014)[7] and Przybyło et al. (2017). 
Combinatorial Nullstellensatz | [formula omitted]-choosable graphs | 1–2–3 conjecture | Total weighting | Maximum average degree
Journal Article
Discrete Mathematics, ISSN 0012-365X, 10/2018, Volume 341, Issue 10, pp. 2661 - 2671
...)-choosable, which implies that the 1–2–3 conjecture is true for such graphs. This improves the results in Cranston et al. (2014)[7] and Przybyło et al. (2017). 
Combinatorial Nullstellensatz | choosable graphs | 1–2–3 conjecture | Total weighting | k,k | Maximum average degree
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 01/2017, Volume 217, pp. 663 - 672
Journal Article
International Journal of Modern Physics A, ISSN 0217-751X, 09/2014, Volume 29, Issue 24, p. 1450135
Journal Article
International Journal of Molecular Sciences, ISSN 1422-0067, 03/2009, Volume 10, Issue 3, pp. 1226 - 1260
Parkinson's disease (PD) is the second most common progressive neurodegenerative disorder after Alzheimer's disease (AD) and represents a large health burden... 
Dat: Dopamine transporter | Pm: Plasmatic membrane | 6-ohda: 6-hydroxydopamine | Gcis: Glial cytoplasmic inclusions | Lns: Lewy neurites | Lbs: Lewy bodies | Cns: Central nervous system | Mptp: 1-methyl 4-phenyl 1, 2, 3, 6 tetrapyridine | Wt: Wild-type | Th: Tyrosine hydroxylase | Nt: Nucleotide(s) | Da: Dopamine | Er: Endoplasmatic reticulum | Irps: Interacting binding proteins | Pld2: Phospholipase d2 | Tfr: Transferrin receptor | 5-utr: 5'-untranslated region | Nac: Non-amyloidogenic component | Gsh: Reduced gluthatione | Ad: Alzheimer's disease | α-syn: Alpha-synuclein | Aa: Amino acid(s) | Dlb: Dementia with lewy bodies | Pd: Parkinson's disease | Ros: Reactive oxygen species | Ire:iron responsive element | PD: Parkinson's disease | ROS: reactive oxygen species | NAC: non-amyloidogenic component | DAT: dopamine transporter | nt: nucleotide(s) | 5-UTR: 5 '-untranslated region | AD: Alzheimer's disease | LBs: Lewy bodies | IRE: iron responsive element | alpha-syn: alpha-synuclein | NEURODEGENERATIVE DISEASES | aa: amino acid(s) | PLD2: phospholipase D2 | MPTP: 1-methyl 4-phenyl 1, 2, 3, 6 tetrapyridine | GCIs: glial cytoplasmic inclusions | MESSENGER-RNA | MITOCHONDRIAL COMPLEX-I | DA: dopamine | 6-OHDA: 6-hydroxydopamine | UP-REGULATION | TISSUE TRANSGLUTAMINASE | BIOCHEMISTRY & MOLECULAR BIOLOGY | TH: tyrosine hydroxylase | TfR: transferrin receptor | LEWY-BODY | SUBSTANTIA-NIGRA | CHEMISTRY, MULTIDISCIPLINARY | DLB: dementia with Lewy Bodies | IRPs: interacting binding proteins | PM: plasmatic membrane | LNs: Lewy neurites | 5'-UNTRANSLATED REGION | GSH: reduced gluthatione | A-BETA COMPONENT | CNS: central nervous system | PRECURSOR PROTEIN | wt: wild-type | ER: endoplasmatic reticulum | Neuroprotective Agents - therapeutic use | Ferric Compounds - toxicity | Levodopa - therapeutic use | Humans | Ferric Compounds - chemistry | Parkinson Disease - drug therapy | Parkinson Disease - physiopathology | alpha-Synuclein - chemistry | Animals | Protein Binding | Parkinson Disease - metabolism | Protein Processing, Post-Translational | alpha-Synuclein - genetics | Lewy Bodies - metabolism | Oxidative Stress - drug effects | alpha-Synuclein - metabolism | RNA - metabolism | 5-UTR: 5'-untranslated region | α-syn: alpha-synuclein | 6 tetrapyridine | MPTP: 1-methyl 4-phenyl 1
Journal Article
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