magic graph; power of graph; factor of graph
Necessary and sufficient conditions for a graph $G$ that its power $G^i$, $i\geq2$, is a magic graph and one consequence are given.
 A. M. Hobbs: Some hamiltonian results in powers of graphs
. J. Res. Nat. Bur. Standards Sect. B 77 (1973), 1-10. MR 0337688
| Zbl 0262.05124
 S. Jezný M. Trenkler: Characterization of magic graphs
. Czechoslovak Math. J. 33 (1983), 435-438. MR 0718926
 L. Nebeský: On 2-factors in squares of graphs
. Czechoslovak Math. J. 29 (1979), 588-594. MR 0548222
 J. Sedláček: Problem 27 in Theory of Graphs and Applications. Proc. Symp. Smolenice. 1963, pp. 163-164.