# 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)

## Abstract

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 language English 1233-1244 12 Acta Mathematica Sinica, English Series 26 7 https://doi.org/10.1007/s10114-010-8517-5 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

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