Control Systems and Computers, N3, 2019, Article 2

https://doi.org/10.15407/csc.2019.03.015

Control Systems and Computers, 2019, Issue 3 (281), pp. 15-22.

UDC 519.1

M.F. SEMENIUTA, PhD in Phys.-Math. Sciences, associate professor, Department of Physics and Mathematics Sciences of the Flight Academy of the National Aviation University,  st. Dobrovolsky, 1, Kropivnitsky, 25005, Ukraine,
marina_semenyuta@ukr.net

Z.OSHERMAN, PhD in Phys.-Math. Sciences, senior lecturer, Department of Medical Physics and Information technology №2 of Donetsk National Medical University,
st. Pryvokzalnaya, 27, Liman, 84404, Donetsk region, Ukraine,
sherman.zoya@gmail.com

ON NEW PROPERTIES OF GRAPHS WITH MAGIC TYPE LABELING

We have shown the connection between vertex labelings of magic graph and its overgraph. Also, we have introduced binary relation on the set of all -distance magic graphs, where , i=1, 2, … and proved, that it is equivalence relation. Therefore, we have explored the properties of the graphs, which are in this relation. Finally, we have offered the algorithm of constructing r-regular handicap graph  of order n, where 0(mod8), r  1,3(mod4) and 3 ≤ r n–5.

Keywords: graph, D-distance magic labeling, (a, d)-distance antimagic labeling, handicap labeling, Ddistance matrix, equivalence relation, 1factor.

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