关于边-多重路替换图的1，2，3-猜想和1，2-猜想(1,2,3-conjecture and 1,2-conjecture for the edge-multiplicity-paths-replacements)
Let f:E(G)→Z+ be an edge-weighting (labeing) of a graph G. For each v∈V(G) ， if yields a proper coloring of the graph, then f is defined as a neighbour-distinguishing edge labeling of G. Let g: V(G) ∪ E(G)→Z+ be a total-weighting (labeing) of a graph G. For each v∈ V(G)，if yields a proper coloring...
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| Format: | Article |
| Language: | zho |
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Zhejiang University Press
2016-11-01
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| Series: | Zhejiang Daxue xuebao. Lixue ban |
| Subjects: | |
| Online Access: | https://doi.org/10.3785/j.issn.1008-9497.2016.06.007 |
| _version_ | 1797235849024241664 |
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| author | LYUDamei(吕大梅) LINWensong(林文松) |
| author_facet | LYUDamei(吕大梅) LINWensong(林文松) |
| author_sort | LYUDamei(吕大梅) |
| collection | DOAJ |
| description | Let f:E(G)→Z+ be an edge-weighting (labeing) of a graph G. For each v∈V(G) ， if yields a proper coloring of the graph, then f is defined as a neighbour-distinguishing edge labeling of G. Let g: V(G) ∪ E(G)→Z+ be a total-weighting (labeing) of a graph G. For each v∈ V(G)，if yields a proper coloring of the graph,then g is defined as a neighbour-distinguishing total labeling of G. For them, there exist two conjectures such as 1,2,3-conjecture (i. e.,every connected graph G≠K2 has a neighbour-distinguishing edge labeling in {1,2,3}) and 1,2-conjecture （i. e.，every simple graph has a neighbour-distinguishing total labeling in {1，2}). This paper shows that 1,2, 3-conjecture and 1, 2-conjecture hold for the edge-multiplicity-paths-replacements for any graph. |
| first_indexed | 2024-04-24T16:54:29Z |
| format | Article |
| id | doaj.art-d08be78463ed4fe9b119d86891ec2bcd |
| institution | Directory Open Access Journal |
| issn | 1008-9497 |
| language | zho |
| last_indexed | 2024-04-24T16:54:29Z |
| publishDate | 2016-11-01 |
| publisher | Zhejiang University Press |
| record_format | Article |
| series | Zhejiang Daxue xuebao. Lixue ban |
| spelling | doaj.art-d08be78463ed4fe9b119d86891ec2bcd2024-03-29T01:58:36ZzhoZhejiang University PressZhejiang Daxue xuebao. Lixue ban1008-94972016-11-0143666867110.3785/j.issn.1008-9497.2016.06.007关于边-多重路替换图的1，2，3-猜想和1，2-猜想(1,2,3-conjecture and 1,2-conjecture for the edge-multiplicity-paths-replacements)LYUDamei(吕大梅)0https://orcid.org/0000-0002-9607-1131LINWensong(林文松)1( 1.School of Science, Nantong University, Nantong 226007, Jiangsu Province, China)( 2.Department of Mathematics, Southeast University, Nanjing 211189, China)Let f:E(G)→Z+ be an edge-weighting (labeing) of a graph G. For each v∈V(G) ， if yields a proper coloring of the graph, then f is defined as a neighbour-distinguishing edge labeling of G. Let g: V(G) ∪ E(G)→Z+ be a total-weighting (labeing) of a graph G. For each v∈ V(G)，if yields a proper coloring of the graph,then g is defined as a neighbour-distinguishing total labeling of G. For them, there exist two conjectures such as 1,2,3-conjecture (i. e.,every connected graph G≠K2 has a neighbour-distinguishing edge labeling in {1,2,3}) and 1,2-conjecture （i. e.，every simple graph has a neighbour-distinguishing total labeling in {1，2}). This paper shows that 1,2, 3-conjecture and 1, 2-conjecture hold for the edge-multiplicity-paths-replacements for any graph.https://doi.org/10.3785/j.issn.1008-9497.2016.06.0071,2 ,3-conjecture1,2-conjectureedge-path-replacement |
| spellingShingle | LYUDamei(吕大梅) LINWensong(林文松) 关于边-多重路替换图的1，2，3-猜想和1，2-猜想(1,2,3-conjecture and 1,2-conjecture for the edge-multiplicity-paths-replacements) Zhejiang Daxue xuebao. Lixue ban 1,2 ,3-conjecture 1,2-conjecture edge-path-replacement |
| title | 关于边-多重路替换图的1，2，3-猜想和1，2-猜想(1,2,3-conjecture and 1,2-conjecture for the edge-multiplicity-paths-replacements) |
| title_full | 关于边-多重路替换图的1，2，3-猜想和1，2-猜想(1,2,3-conjecture and 1,2-conjecture for the edge-multiplicity-paths-replacements) |
| title_fullStr | 关于边-多重路替换图的1，2，3-猜想和1，2-猜想(1,2,3-conjecture and 1,2-conjecture for the edge-multiplicity-paths-replacements) |
| title_full_unstemmed | 关于边-多重路替换图的1，2，3-猜想和1，2-猜想(1,2,3-conjecture and 1,2-conjecture for the edge-multiplicity-paths-replacements) |
| title_short | 关于边-多重路替换图的1，2，3-猜想和1，2-猜想(1,2,3-conjecture and 1,2-conjecture for the edge-multiplicity-paths-replacements) |
| title_sort | 关于边 多重路替换图的1 2 3 猜想和1 2 猜想 1 2 3 conjecture and 1 2 conjecture for the edge multiplicity paths replacements |
| topic | 1,2 ,3-conjecture 1,2-conjecture edge-path-replacement |
| url | https://doi.org/10.3785/j.issn.1008-9497.2016.06.007 |
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