Introduction to connecting coalitions

A connecting coalition in a graph [Formula: see text] consists of two disjoint vertex subsets [Formula: see text] and [Formula: see text] of [Formula: see text], where neither [Formula: see text] nor [Formula: see text] is a connected graph but [Formula: see text] is a connected graph. A connecting coalition partition is a vertex partition [Formula: see text], and the maximum cardinality of all possible [Formula: see text] is called the connecting coalition number, [Formula: see text]. Some bounds on the coalition number [Formula: see text] are found, and graphs having [Formula: see text] are characterized. Further, the existence of connecting coalition partitions in graphs is explored.