Note on the Coalition Number of the dth Power of the n-Path

In a graph $G=\left(V,E\right)$ , two disjoint sets $V_1,V_2？V$ are said to form a coalition, if neither $V_1$ nor $V_2$ is a dominating set of $G$ , but $V_1\cup V_2$ is a dominating set of $G$ . The sets $V_1$ and $V_2$ forming a coalition are said to be coalition partners. A coalition partition, called a c-partition, is a vertex partition $\pi =\left\{V_1,V_2,？,V_k\right\}$ such that each $V_i\in \pi$ satisfies the following conditions: $V_i$ is a singleton dominating set of $G$ , or $V_i$ is not a dominating set of $G$ but has a coalition partner