total coalitions of cubic graphs of order at most 10

A total coalition in a graph $g=(v,e)$ consists of two disjoint sets of vertices $v_{1}$ and $v_{2}$, neither of which is a total dominating set but whose union $v_{1}cup v_{2}$, is a total dominating set. a total coalition partition in a graph $g$ of order $n=|v|$ is a vertex partition $tau = {v_1, v_2, dots , v_k }$ such that every set $v_i in tau$ is not a total dominating set but forms a total coalition with another set $v_jin tau$ which is not a total dominating set. the total coalition number $tc(g)$ equals the maximum $k$ of a total coalition partition of $g$. in this paper, we determine the total coalition number of all cubic graphs of order $n le 10$.