Full friendly index sets of Cartesian products of two cycles

Wai Chee SHIU, Man Ho Ling

Research output: Contribution to journalJournal articlepeer-review

16 Citations (Scopus)


Let G = (V,E) be a connected simple graph. A labeling f: V → Z2 induces an edge labeling f*: E → Z2 defined by f*(xy) = f(x)+ f(y) for each xy ∈ E. For i ∈ Z2, let υf(i) = {pipe}f-1(i){pipe} and ef(i) = {pipe}f*-1(i){pipe}. A labeling f is called friendly if {pipe}υf(1) - υf(0){pipe} ≤ 1. For a friendly labeling f of a graph G, we define the friendly index of G under f by if(G) = ef(1) - ef(0). The set {if(G) {pipe} f is a friendly labeling of G} is called the full friendly index set of G, denoted by FFI(G). In this paper, we will determine the full friendly index set of every Cartesian product of two cycles.

Original languageEnglish
Pages (from-to)1233-1244
Number of pages12
JournalActa Mathematica Sinica, English Series
Issue number7
Publication statusPublished - Jul 2010

Scopus Subject Areas

  • Mathematics(all)
  • Applied Mathematics

User-Defined Keywords

  • Cartesian product of two cycles
  • Friendly index set
  • Friendly labeling
  • Vertex labeling


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