Graphs with isolation number equal to one third of the order

Magdalena Lemańska; Merce Mora; Maria Jose Souto Salorio

doi:10.1016/j.disc.2024.113903

Graphs with isolation number equal to one third of the order

Abstract

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.

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Authors (3)

Magdalena Lemańska dr inż.
- Faculty of Applied Physics and Mathematics
- Gdańsk University of Technology
Merce Mora Prof
Maria Jose Souto Salorio Prof

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Category:

Articles

Type:

artykuły w czasopismach

Published in:

DISCRETE MATHEMATICS no. 347,
ISSN: 0012-365X

Language:

English

Publication year:

2024

Bibliographic description:

Lemańska M., Mora M., Souto Salorio M. J.: Graphs with isolation number equal to one third of the order// DISCRETE MATHEMATICS -Vol. 347,iss. 5 (2024), s.113903-

DOI: