Hamiltonicity of 3tEC Graphs with α=κ+1
A set S of vertices in a graph G is a total dominating set of G if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set of G is the total domination number γtG of G. The graph G is total domination edge-critical, or γtEC, if for every edge e in the com...
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Hindawi Limited
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/5523761 |
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doaj-f1b96c309581499d993da09be6eda3012021-05-03T00:00:02ZengHindawi LimitedJournal of Mathematics2314-47852021-01-01202110.1155/2021/5523761Hamiltonicity of 3tEC Graphs with α=κ+1Huanying He0Xinhui An1Zongjun Zhao2College of ScienceCollege of Mathematics and System ScienceCollege of ScienceA set S of vertices in a graph G is a total dominating set of G if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set of G is the total domination number γtG of G. The graph G is total domination edge-critical, or γtEC, if for every edge e in the complement of G, γtG+e<γtG. If G is γtEC and γtG=k, we say that G is ktEC. In this paper, we show that every 3tEC graph with δG≥2 and αG=κG+1 has a Hamilton cycle.http://dx.doi.org/10.1155/2021/5523761 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Huanying He Xinhui An Zongjun Zhao |
| spellingShingle |
Huanying He Xinhui An Zongjun Zhao Hamiltonicity of 3tEC Graphs with α=κ+1 Journal of Mathematics |
| author_facet |
Huanying He Xinhui An Zongjun Zhao |
| author_sort |
Huanying He |
| title |
Hamiltonicity of 3tEC Graphs with α=κ+1 |
| title_short |
Hamiltonicity of 3tEC Graphs with α=κ+1 |
| title_full |
Hamiltonicity of 3tEC Graphs with α=κ+1 |
| title_fullStr |
Hamiltonicity of 3tEC Graphs with α=κ+1 |
| title_full_unstemmed |
Hamiltonicity of 3tEC Graphs with α=κ+1 |
| title_sort |
hamiltonicity of 3tec graphs with α=κ+1 |
| publisher |
Hindawi Limited |
| series |
Journal of Mathematics |
| issn |
2314-4785 |
| publishDate |
2021-01-01 |
| description |
A set S of vertices in a graph G is a total dominating set of G if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set of G is the total domination number γtG of G. The graph G is total domination edge-critical, or γtEC, if for every edge e in the complement of G, γtG+e<γtG. If G is γtEC and γtG=k, we say that G is ktEC. In this paper, we show that every 3tEC graph with δG≥2 and αG=κG+1 has a Hamilton cycle. |
| url |
http://dx.doi.org/10.1155/2021/5523761 |
| work_keys_str_mv |
AT huanyinghe hamiltonicityof3tecgraphswithak1 AT xinhuian hamiltonicityof3tecgraphswithak1 AT zongjunzhao hamiltonicityof3tecgraphswithak1 |
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