Graceful 2-regular graphs and Skolem sequences

Jaromir Abrham
1991 Discrete Mathematics  
Abrham. J.. Graceful 2-regular graphs and Skolem sequences, Discrete Mathematics 93 (1991) 115-121. The purpose of the paper is to study relations graphs and certain Skolem sequences. between graceful numbering of certain 2-regular In this paper, all graphs will be finite, without loops or multiple edges. For any graph G, the symbols V(G) and E(G) will denote its vertex set and its edge set, respectively. A graceful numbering of a graph G with m vertices and n edges is a one-to-one mapping q of
more » ... the set V(G) into the set (0, 1, . . . , n } which has the property that the values of the edges form the set {I, 2, . . . , n} if the value g(e) of the edge e with the end vertices u, u is defined by g(e) = Iv(u) -r/~(u)l. A graph is called graceful if it has a graceful numbering. An cu-valuation 1~ of a graph G is a graceful numbering of G which satisfies the following additional condition: There exists a number r (OS r s ]E(G)]) such that for any edge e = (v, w),
doi:10.1016/0012-365x(91)90247-y fatcat:o4l4ikoicjhbvmfmg344ja6soa