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Edge-gracefulness of the composition of paths with null graphs

Authors
Journal
Discrete Mathematics
0012-365X
Publisher
Elsevier
Publication Date
Volume
253
Identifiers
DOI: 10.1016/s0012-365x(01)00449-6
Keywords
  • Edge-Graceful
  • Composition Of Graph
  • Labeling Matrix

Abstract

Abstract Let G = (V,E) be a ( p, q)-graph. Let f : E→{1,2,…,q} be a bijection. The induced mapping f + : V→ Z p of f is defined by f +(u)≡ ∑ uv∈E f(uv) ( 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 P m ∘ N n , where there are mn vertices and ( m−1) n 2 edges. We show that P 3∘ N n is edge-graceful if n is odd.

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