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Skolem labelled graphs

โœ Scribed by E. Mendelsohn; N. Shalaby


Publisher
Elsevier Science
Year
1991
Tongue
English
Weight
814 KB
Volume
97
Category
Article
ISSN
0012-365X

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Lee, S.M. and SC. Shee, On Skolem graceful graphs, Discrete Mathematics 93 (1991) 195-200. A Skolem graceful labelling of graphs is introduced. It is shown that a tree is Skolem graceful iff it is graceful. The Skolem deficiency of a graph is defined and Skolem deficiencies of some well-known graphs

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A k-extended Skolem sequence of order n is an integer sequence (s,, s2,. . . , S Z ~+ ~) in which sk = 0 and for eachj E (1,. . . ,n}, there exists a unique i E (1,. . . ,2n} such that si = s i + j = j . We show that such a sequence exists if and only if either 1) k is odd and n = 0 or 1 (mod 4) or