## Abstract

Let

*G*= (*V*,*E*) be a connected simple graph. A labeling*ƒ*:*V*→ Z_{2}induces an edge labeling*ƒ** :*E*→ Z_{2}defined by*ƒ**(*xy*) =*ƒ*(*x*) +*ƒ*(*y*) for each*xy*∈*E*. For*i*∈ Z_{2}, let*v*(_{ƒ}*i*) = |*ƒ*^{-1}(*i*)| and e*(*_{ƒ}*i*) = |*ƒ**^{-1}(*i*)|. If |*v**(1)-*_{ƒ}*v**(0)| ≤ 1, then*_{ƒ}*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*i*(_{ƒ}*G*) =*e**(1) -*_{ƒ}*e**(0). The set {*_{ƒ}*i**(*_{ƒ}*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 language | English |
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Pages (from-to) | 65-75 |

Number of pages | 11 |

Journal | Congressus Numerantium |

Volume | 197 |

Publication status | Published - Jul 2009 |

## User-Defined Keywords

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

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