## Abstract

Let G = (V,E) be a connected simple graph. A labeling f: V → Z_{2} induces an edge labeling f*: E → Z_{2} defined by f*(xy) = f(x)+ f(y) for each xy ∈ E. For i ∈ Z_{2}, let υ_{f}(i) = {pipe}f^{-1}(i){pipe} and e_{f}(i) = {pipe}f*^{-1}(i){pipe}. A labeling f is called friendly if {pipe}υ_{f}(1) - υ_{f}(0){pipe} ≤ 1. For a friendly labeling f of a graph G, we define the friendly index of G under f by i_{f}(G) = e_{f}(1) - e_{f}(0). The set {i_{f}(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 language | English |
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Pages (from-to) | 1233-1244 |

Number of pages | 12 |

Journal | Acta Mathematica Sinica, English Series |

Volume | 26 |

Issue number | 7 |

DOIs | |

Publication status | Published - Jul 2010 |

## Scopus Subject Areas

- Mathematics(all)
- Applied Mathematics

## User-Defined Keywords

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