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

Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Full friendly index sets of Cartesian products of two cycles

Language

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

Publication Date

2010

Source Publication Title

Acta Mathematica Sinica

Volume

26

Issue

7

Start Page

1233

End Page

1244

Publisher

Springer Verlag

ISSN (print)

14398516

ISSN (electronic)

14397617

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