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Extremal Graphs for the K1,2-Isolation Number of Graphs.
- Source :
-
Bulletin of the Malaysian Mathematical Sciences Society . Jul2024, Vol. 47 Issue 4, p1-26. 26p. - Publication Year :
- 2024
-
Abstract
- For any non-negative integer k and any graph G, a subset S ⊆ V (G) is said to be a K 1 , k + 1 -isolating set of G if G - N [ S ] does not contain K 1 , k + 1 as a subgraph. The K 1 , k + 1 -isolation number of G, denoted by ι k (G) , is the minimum cardinality of a K 1 , k + 1 -isolating set of G. Recently, Zhang and Wu (2021) proved that if G is a connected n-vertex graph and G ∉ { P 3 , C 3 , C 6 } , then ι 1 (G) ≤ 2 7 n . In this paper, we characterize all extremal graphs attaining this bound, which resolves a problem proposed by Zhang and Wu (Discrete Appl Math 304:365–374, 2021). [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01266705
- Volume :
- 47
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Bulletin of the Malaysian Mathematical Sciences Society
- Publication Type :
- Academic Journal
- Accession number :
- 177544160
- Full Text :
- https://doi.org/10.1007/s40840-024-01711-6