Total isolation of k-cliques in a graph
For a graph G=(V(G),E(G)) and any positive integer k, a set D⊆V(G) is called a total k-clique isolating set of G if G−N[D] contains no k-clique and D induces a subgraph with no vertex of degree 0. The total k-clique isolation number ιt(G,k) is the minimum cardinality of a total k-clique isolating se...
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| Published in | Discrete mathematics Vol. 348; no. 12; p. 114689 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.12.2025
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0012-365X |
| DOI | 10.1016/j.disc.2025.114689 |
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| Abstract | For a graph G=(V(G),E(G)) and any positive integer k, a set D⊆V(G) is called a total k-clique isolating set of G if G−N[D] contains no k-clique and D induces a subgraph with no vertex of degree 0. The total k-clique isolation number ιt(G,k) is the minimum cardinality of a total k-clique isolating set of G. Clearly, ιt(G,1) is the total domination number of G, and ιt(G,2) was investigated by Boyer, Goddard and Henning recently. In this paper, we prove that for k≥3 and n≥k+2, if G is a connected graph of order n, then ιt(G,k)≤2nk+2. The bound is sharp. |
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| AbstractList | For a graph G=(V(G),E(G)) and any positive integer k, a set D⊆V(G) is called a total k-clique isolating set of G if G−N[D] contains no k-clique and D induces a subgraph with no vertex of degree 0. The total k-clique isolation number ιt(G,k) is the minimum cardinality of a total k-clique isolating set of G. Clearly, ιt(G,1) is the total domination number of G, and ιt(G,2) was investigated by Boyer, Goddard and Henning recently. In this paper, we prove that for k≥3 and n≥k+2, if G is a connected graph of order n, then ιt(G,k)≤2nk+2. The bound is sharp. |
| ArticleNumber | 114689 |
| Author | Cao, Yupei Wu, Baoyindureng An, Xinhui |
| Author_xml | – sequence: 1 givenname: Yupei surname: Cao fullname: Cao, Yupei – sequence: 2 givenname: Xinhui orcidid: 0000-0003-2048-0497 surname: An fullname: An, Xinhui email: xjaxh@163.com – sequence: 3 givenname: Baoyindureng surname: Wu fullname: Wu, Baoyindureng |
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| Snippet | For a graph G=(V(G),E(G)) and any positive integer k, a set D⊆V(G) is called a total k-clique isolating set of G if G−N[D] contains no k-clique and D induces a... |
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| SubjectTerms | Clique Total domination number Total isolating set |
| Title | Total isolation of k-cliques in a graph |
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