Edge-criticality in trees upon outer connected independence.

In a graph G = (V,E)(not necessarily connected), an independent set S ⊆ V is said to be an <italic>outer-connected independent set</italic> if ω(G − S) ≤ ω(G), where ω(G) is the number of components in G. The maximum cardinality of an outer connected independent set is called the <italic>outer-connected independence number</italic> and is denoted by Ioc(G). This concept was introduced in [I. Sahul Hamid, R. Gnanaprahasam and M. Fatima Mary, Outer connected independence in graphs, <italic>Discrete Math. Algor. Appl.</italic> <bold>7</bold>(3) (2015), Article ID: 1550039, 11 pp., doi: 10.1142/S1793830915500391], and as a continuation of this work, the effect of Ioc on edge removal was reported in [M. Fatima Mary, A. Anitha and I. Sahul Hamid, Edge-criticality in unicyclic graphs upon outer connected independence, <italic>Adv. Appl. Math. Sci.</italic> <bold>21</bold>(8) (2022) 4221–4238] and [I. Sahul Hamid and M. Fatima Mary, Criticality of outer connected independence upon edge removal, <italic>Electron. Notes Discr. Math.</italic> <bold>63</bold> (2017) 361–369]. This paper presents a further study of the critical edges upon Ioc in trees. [ABSTRACT FROM AUTHOR]