I am not sure to understand what do you try to do ( your column names are duplicated and this is confusing). You can try this for example:
df = expand.grid( yvert= seq_len(dimy),xver= seq_len(dimy))
transform(df,xvert1=xvert,yvert1=yvert+1)
CGW added for completeness' sake: generate both horizontal and vertical walls:
df = expand.grid( xvert= seq_len(dimx),yvert= seq_len(dimy))
transform(df,xvert1=xvert,yvert1=yvert+1) ->dfv
df2 <- expand.grid(yvert= seq_len(dimy), xvert= seq_len(dimx))
transform(df2,yvert1=yvert,xvert1=xvert+1) ->dfh
# make x,y same order in both arrays
dfh[] <- dfh[,c(2,1,4,3)]