On new proprties of graphs with magic type labeling

Abstract

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 Di-distance magic graphs, where Di ⊂ {0, 1, ..., d}, 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 G = (V, E) of order n, where n ≡ 0(mod8), r ≡ 1,3(mod4) and 3 ≤ r ≤ n–5.