You could start each row with a yo. Have the yarn in front when you knit the first stitch and it will create a loop for the edge stitch. I'd suggest adding a one-stitch garter stitch edge (knit every row) on each side of the scarf to keep the two edges looking the same.
It will increase your stitch number, though, so starting on row 3, yo, work across the row and knit the last two stitches together. Keep going in this manner.
"Trust the pattern!"
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IngridKH on Ravelry