Edge-gracefulness of the composition of paths with null graphs

  • Authors:

  • Wai Chee Shiu;Peter Che Bor Lam;Hee Lin Cheng

  • Affiliations:

  • Department of Mathematics, Hong Kong Baptist University, 224 Waterloo Road, Kowloon Tong, Hong Kong;Department of Mathematics, Hong Kong Baptist University, 224 Waterloo Road, Kowloon Tong, Hong Kong;Department of Mathematics, Hong Kong Baptist University, 224 Waterloo Road, Kowloon Tong, Hong Kong

  • Venue:
  • Discrete Mathematics
  • Year:
  • 2002

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Abstract

Let G = (V,E) be a (p,q)-graph. Let f:E → {1,2,..., q} be a bijection. The induced mapping f+ : V → Zp of f is defined by f+(u) ≡ Σuυ∈Ef(uυ) (modp) for u ∈ V. If f+ is a bijection, then G is called edge-graceful. In this paper, we investigate the edge-gracefulness of the composition of paths with null graphs Pm Nn, where there are mn vertices and (m - 1)n2 edges. We show that P3 Nn is edge-graceful if n is odd.