A set D of vertices of a graph G is isolating if the set of vertices not
in D or with no neighbor in D is independent. The isolation number of G,
denoted by ι(G), is the minimum cardinality of an isolating set of G.
It is known that ι(G)≤n/3, if G is a connected graph of order n,
n≥3, distinct from C5. 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.Comment: 15 pages, 12 figure