A set D of vertices of a graph G is isolating if the set of vertices not in D and with no neighbor in D is independent. The isolation number of G, denoted by \iota(G) , is the minimum cardinality of an isolating set of G. It is known that \iota(G) \leq n/3 , if G is a connected graph of order n, , distinct from C_5 . The main result of this work is the characterisation of unicyclic and block graphs of order n with isolating number equal to n/3 . Moreover, we provide a family of general graphs attaining this upper bound on the isolation number.
Authors
- dr inż. Magdalena Lemańska link open in new tab ,
- Prof Merce Mora,
- Prof Maria Jose Souto Salorio
Additional information
- DOI
- Digital Object Identifier link open in new tab 10.1016/j.disc.2024.113903
- Category
- Publikacja w czasopiśmie
- Type
- artykuły w czasopismach
- Language
- angielski
- Publication year
- 2024
