Abstract. We have generalized the results for corona Pn º P 1, which make it possible to state that Pn º P 1 is not an (a, d )-distance antimagic graph for all a and d. We have obtained the condition for the existence of an (a, d )-distance antimagic labeling of a hypercube Qn. We found functional relationships that generate this type of labeling for Qn and used the method of mathematical induction to prove that Qn is a (2n+n –1, n –2)-distance antimagic graph. We have defined two types of graphs that do not allow 1-vertex bimagic vertex labeling. We also established a relation between the distance magic labeling of a regular graph G with 1-vertex bimagic vertex labeling G ∪G.
Keywords: distance magic labeling, (a, d )-distance antimagic labeling, 1-vertex bimagic vertex labeling, n-dimensional cube, crown.
Flight Academy of the National Aviation University, Kropyvnytskyi, Ukraine,
e-mail: marina_semenyuta@ukr.net.