In this paper, we continue the study of 
the concept of $g^{\#}\alpha$-closed sets, $g^{\#}\alpha$-open 
sets and digital planes \Zpl\ (cf.\ \cite{Devi04}).  
In 1970, E.D. Khalimsky \cite{K1} 
introduced the concept of the digital line or so called {\it Khalimsky line} 
$(\mathbb{Z},\kappa)$.  The digital plane \Zpl\ (eg. \cite{KK94}) is the topological 
product of two copies of $(\mathbb{Z},\kappa)$.  A subset $A$ of a topological space 
$(X,\tau)$ is said to be $g^{\#}\alpha$-closed \cite{Devi04}, if $\alpha Cl(A)\subset 
U$ whenever $A\subset U$ and $U$ is g-open set of $(X,\tau)$.  The complement of 
a $g^{\#}\alpha$-closed set is said to be a $g^{\#}\alpha$-open set of $(X,\tau)$.  
The $g^{\#}\alpha$-openness in \Zpl\ is characterized (cf. Theorem~\ref{t100} (ii)): 
for a subset $B$ with some closed singletons of \Zpl, $B$ is $g^{\#}\alpha$-open 
in \Zpl\ if and only if $(U(x))_{\kappa^{2}}\subset B$ holds for each 
closed singleton $\{x\}\subset B$, where $U(x)$ is the smallest open set 
containing $x$.  
The family of 
all $g^{\#}\alpha$-open sets of \Zpl, say $G^{\#}\alpha O$, 
forms an alternative topology of ${\mathbb{Z}}^{2}$ (cf.\ Theorem A, Corollary B (i)).  
Let $({\mathbb{Z}}^{2}, G^{\#}\alpha O)$ be a topological space obtained 
by changing the topology $\kappa^{2}$ of the digital plane \Zpl\ 
by $G^{\#}\alpha O$.  We prove that 
this plane $({\mathbb{Z}}^{2} , G^{\#}\alpha O)$ is a $T_{1/2}$-space 
(cf.\ Corollary B (ii) (ii-1), Remark 3.5); moreover it is shown that 
the plane $({\mathbb{Z}}^{2}, G^{\#}\alpha O)$ is $T_{3/4}$ (cf. Corollary B (ii) (ii-2)).  
It is well known that the digital plane \Zpl\ is not $T_{1/2}$ even if 
$(\mathbb{Z}, \kappa)$ 
is $T_{1/2}$.