Cybernetics and Systems Analysis

, Volume 54, Issue 2, pp 295–301 | Cite as

On (a, d )-Distance Anti-Magic and 1-Vertex Bimagic Vertex Labelings of Certain Types of Graphs

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Abstract

The results for the corona P n  ∘ P1 are generalized, which make it possible to state that P n  ∘ P1 is not an ( a, d)-distance antimagic graph for arbitrary values of a and d. A condition for the existence of an ( a, d)-distance antimagic labeling of a hypercube Q n is obtained. Functional dependencies are found that generate this type of labeling for Q n . It is proved by the method of mathematical induction that Q n is a (2 n  + n − 1, n − 2) -distance antimagic graph. Three types of graphs are defined that do not allow a 1-vertex bimagic vertex labeling. A relation between a distance magic labeling of a regular graph G and a 1-vertex bimagic vertex labeling of G ∪ G is established.

Keywords

distance magic labeling ( a, d) -distance antimagic labeling 1-vertex bimagic vertex labeling n-dimensional cube corona 
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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Flight Academy of the National Aviation UniversityKropyvnytskyiUkraine

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