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Cybernetics And Systems Analysis
International Theoretical Science Journal
UDC 519.17
М.F. Semeniuta

ON (a, d )-DISTANCE ANTIMAGIC AND 1-VERTEX BIMAGIC VERTEX LABELINGS
OF CERTAIN TYPES OF GRAPHS

Abstract. We have generalized the results for corona Pn º P1, which make it possible to state that Pn º P1 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.



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Flight Academy of the National Aviation University, Kropyvnytskyi, Ukraine,
e-mail: marina_semenyuta@ukr.net.

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