Contents

Ars Combinatoria

  • Research article

Gracefulness of the Union of Cycles and Paths

M.A. Seoud1, A.E.I.Abd el Maqsoud1, J. Sheehan2
1Faculty of Science Ain Shams University Abbassia Cairo Egypt
2Department of Mathematical Sciences University of Aberdeen Aberdeen Scotland
  • Published: 31/01/2000

Abstract

Frucht and Salinas [1] conjectured that \(C(k) \cup P(n)\) (\(n \geq 3\)) is graceful if and only if \(k + n \geq 7\). We prove that \(C(2k) \cup P(n)\) is graceful for \(n > k + 1\) (\(k \geq 3\)).

For smaller cases we prove that \(C(2k) \cup P(n)\) is graceful for \(k = 3, 4, 5, 6; n \geq 2\).

Citation
M.A. Seoud, A.E.I.Abd el Maqsoud, J. Sheehan. Gracefulness of the Union of Cycles and Paths[J], Ars Combinatoria, Volume 054. 283-292. .