## Abstract

Let G = (V, E) be a graph, a vertex 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 each i ∈ Z_{2}, define v_{f} (i) = | f^{- 1} (i) | and e_{f} (i) = | f^{*- 1} (i) |. We call f friendly if | v_{f} (1) - v_{f} (0) | ≤ 1. The full friendly index set of G is the set of all possible values of e_{f} (1) - e_{f} (0), where f is friendly. In this note, we study the full friendly index set of the grid graph P_{2} × P_{n}.

Original language | English |
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Pages (from-to) | 3688-3693 |

Number of pages | 6 |

Journal | Discrete Mathematics |

Volume | 308 |

Issue number | 16 |

DOIs | |

Publication status | Published - 28 Aug 2008 |

## Scopus Subject Areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

## User-Defined Keywords

- Friendly index
- Grid

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