Extreme Friendly Indices of C× Pn

Wai Chee Shiu, Fook Sun Wong

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Let G = (V,E) be a connected simple graph. A labeling ƒ: → Z2 induces an edge labeling ƒ* : E → Z2 defined by ƒ*(xy) = ƒ(x) + ƒ(y) for each xy ∈ E. For i ∈ Z2, let vƒ(i) = |ƒ-1(i)| and eƒ(i) = |ƒ*-1(i)|. If |vƒ(1)-vƒ(0)| ≤ 1, then ƒ is called a friendly labeling of G. For a friendly labeling f of a graph G, we define the friendly index of G under ƒ by iƒ(G) = eƒ(1) - eƒ(0). The set {iƒ(G)|ƒ is a friendly labeling of G} is called the full friendly index set of G. In this paper, we will present the extreme friendly indices, i.e., the maximum and minimum friendly indices of Cartesian product of a cycle and a path.
Original languageEnglish
Pages (from-to)65-75
Number of pages11
JournalCongressus Numerantium
Publication statusPublished - Jul 2009

User-Defined Keywords

  • Vertex labeling
  • friendly labeling
  • friendly index set
  • Cartesian product of a cycle and a path


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