The game chromatic index of special graphs

In this paper, the game chromatic index K
2
,n
, Cartesian product P
2
□P
n
and P
2
□S
n
is studied, where K
2
,n
is a complete bipartite graph, P
n
is a path on n vertices and S
n
is a star graph of order n + 1. It is proved that $\chi_g^\prime (K_{2,n}) = \chi_g^\prime (P_2 \square S_n) = n + 1$ for n ≥ 2, $\chi_g^\prime (P_2 \square P_n) = 3$ for n = 2, 3 and $\chi_g^\prime (P_2 \square P_n) = 4$ for n ≥ 4.