Full friendly index sets of Cartesian products of two cycles

Wai Chee Shiu; Man Ho Ling

doi:10.1007/s10114-010-8517-5

Full friendly index sets of Cartesian products of two cycles

Wai Chee Shiu, Man Ho Ling

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-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 υ_f(i) = {pipe}f^-1(i){pipe} and e_f(i) = {pipe}f*^-1(i){pipe}. A labeling f is called friendly if {pipe}υ_f(1) - υ_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) {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
Pages (from-to)	1233-1244
Number of pages	12
Journal	Acta Mathematica Sinica, English Series
Volume	26
Issue number	7
DOIs	https://doi.org/10.1007/s10114-010-8517-5
Publication status	Published - Jul 2010

User-Defined Keywords

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

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10.1007/s10114-010-8517-5

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title = "Full friendly index sets of Cartesian products of two cycles",

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.",

keywords = "Cartesian product of two cycles, Friendly index set, Friendly labeling, Vertex labeling",

author = "Shiu, {Wai Chee} and Ling, {Man Ho}",

note = "Funding Information: Received October 17, 2008, Accepted April 9, 2009 Supported by FRG/07-08/II-55 Hong Kong Baptist University",

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AU - Shiu, Wai Chee

AU - Ling, Man Ho

N1 - Funding Information: Received October 17, 2008, Accepted April 9, 2009 Supported by FRG/07-08/II-55 Hong Kong Baptist University

PY - 2010/7

Y1 - 2010/7

N2 - 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.

AB - 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.

KW - Cartesian product of two cycles

KW - Friendly index set

KW - Friendly labeling

KW - Vertex labeling

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DO - 10.1007/s10114-010-8517-5

M3 - Journal article

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SN - 1439-8516

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JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

IS - 7

ER -

Full friendly index sets of Cartesian products of two cycles

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