Less amount of bulk is easier to deal with for a dog, human bandanas are usually square, but doggie (and kitty) ones are just equilateral triangles. If you have a sewing machine, hemming the edges is pretty simple, and most effective at preventing fraying, but if you do not, pinking shears are the next best thing. A woven fabric with fray more readily than a knit of any sort, but the fabrics we use to make bandanas - the ones with pretty patterns, are almost always woven.