## 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 v _{f}(i) = {pipe}f ^{-1}(i){pipe} and e _{f}(i) = {pipe}(f ^{+}) ^{-1}(i){pipe}. A labeling f is called friendly if {pipe}v _{f}(1)-v _{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)f is a friendly labeling of G} is called the full friendly index set of G, denoted by FFI(G). In this paper, we determine the full friendly index sets of cylinder graphs C _{m} × P _{n} for even m ≥ 4, even n ≥ 4 and m ≤ 2n. We also list the results of other cases for m, n ≥ 4.

Original language | English |
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Pages (from-to) | 141-162 |

Number of pages | 22 |

Journal | Australasian Journal of Combinatorics |

Volume | 52 |

Publication status | Published - Feb 2012 |

## Scopus Subject Areas

- Discrete Mathematics and Combinatorics