Support Strong Coalition in Graphs

This paper introduces the concept of support strong coalition in graphs, based on the concept of support. For a graph [Formula: see text], a subset [Formula: see text] is called a support strong dominating set of [Formula: see text], if for every vertex [Formula: see text] there exists a vertex [Formula: see text] such that [Formula: see text] and [Formula: see text]. A support strong coalition consists of two disjoint vertex sets that are not support strong dominating sets individually, but whose union forms a support strong dominating set. We further introduce support strong coalition partitions and define the support strong coalition number of a graph as the maximum cardinality of such a partition. The structural properties of these concepts are analyzed, and results are established for several standard classes of graphs. This work extends the framework of coalition - based domination and provides new directions for research in graph domination theory.