On k-graceful, countably infinite graphs (Q1078581)

Generalizing the concept ''k-graceful graph'' by considering countably infinite graphs instead of finite graphs, the author investigates k- graceful and bijective-k-graceful graphs for each \(k\in {\mathbb{N}}\). Similarly to his paper with the title ''Problems in graph theory: Graceful and sequential numberings of infinite graphs'' published in Southeast. Asian Bull. Math. 9, 15-22 (1985; Zbl 0589.05057), he determines some classes of k-graceful and bijective-k-graceful graphs, presents several sufficient conditions for graphs to be k-graceful or bijective-k- graceful, and finally shows a relation between k-gracefulness of countably infinite graphs and certain problems of number theory.