  For a graph $G=(V,E)$, a set $D\subset V(G)$ is a strong dominating set of
$G$, if for every vertex $x\in V (G)\setminus D$ there is a vertex $y\in D$
with $xy \in E(G)$ and $deg(x)\leq deg(y)$. A strong coalition consists of two
disjoint sets of vertices $V_{1}$ and $V_{2}$, neither of which is a strong
dominating set but whose union $V_{1}\cup V_{2}$, is a strong dominating set. A
vertex partition $\Omega=\{V_1, V_2,..., V_k \}$ of vertices in $G$ is a strong
coalition partition, if every set $V_i \in\Omega$ either is a strong dominating
set consisting of a single vertex of degree $n-1$, or is not a strong
dominating set but produces a strong coalition with another set $V_j \in
\Omega$ that is not a strong dominating set. The maximum cardinality of a
strong coalition partition of $G$ is the strong coalition number of $G$ and is
denoted by $SC(G)$. In this paper, we study properties of strong coalitions in
graphs.
