## HKBU Staff Publication

Journal Article

#### Department/Unit

Department of Mathematics

#### Title

Full friendly index sets of Cartesian products of two cycles

English

#### 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. © 2010 Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg.

#### Keywords

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

2010

#### Source Publication Title

Acta Mathematica Sinica

26

7

1233

1244

Springer Verlag

#### DOI

10.1007/s10114-010-8517-5

http://dx.doi.org/10.1007/s10114-010-8517-5

14398516

14397617

COinS