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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/5523761 |
| Summary: | 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. |
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| ISSN: | 2314-4785 |