Extensions of Graceful Valuations of $2$-Regular Graphs Consisting of $4$-Gons

¹ Dept. of Industrial Engineering, University of Toronto, Toronto, Ontario, Canada M5S 1A4

²Département de mathématiques et de statistique, Université de Montréal, C.P. 6128, Succursale “A” Montréal, Québec, Canada H3C 337