There are many mother goose books. I attempted to look for all the ones in my collection that fit your description. The characters around the edge lead me to believe it is a golden book. I would suggest you go to www.ebay.com and search for mother goose golden book. Maybe if you see the cover , you can find the book.
I am trying to identify a Golden Book my family had as a child the front cover is now missing but we do however still have the back cover and some of the spine. The spine is green and yellow and we believe is an old mother goose version the back cover is yellow with characters around the edge. It is about a half inch thick and measures 9.5 inches x 12.5 inches roughly has 96 pages and somewhere around 330 nursery rhymes. The illustrations are around early 1970's late 1960's and was gifted to us in early 1970. Please help identify this old family heirloom and if it is still avalible. Do have pictures just can't figure out how to post them!