Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

Abstract

Let $G=(V,E)$ be a connected simple graph. A labeling $f:Vrightarrow Z_2$ induces an edgelabeling $f^*:EtoZ_2$ defined by $f^*(xy)=f(x)+f(y)$ for each $xy in E$. For $iinZ_2$,let $v_f(i)=|f^{-1}(i)|$ and $e_f(i)=|f^{*-1}(i)|$. A labeling $f$ is called friendly if$|v_f(1)-v_f(0)|le 1$. The full friendly index set of $G$ consists all possible differencesbetween the number of edges labeled by 1 and the number of edges labeled by 0. In recent years,full friendly index sets for certain graphs were studied, such as tori, grids $P_2times P_n$,and cylinders $C_mtimes P_n$ for some $n$ and $m$. In this paper we study the full friendlyindex sets of cylinder graphs $C_mtimes P_2$ for $mgeq 3$, $C_mtimes P_3$ for $mgeq 4$and $C_3times P_n$ for $ngeq 4$. The results in this paper complement the existing resultsin literature, so the full friendly index set of cylinder graphs are completely determined.

Keywords

Full friendly index sets, friendly labeling, cylinder graphs

Publication Date

12-2013

Source Publication Title

Transactions on Combinatorics

Volume

2

Issue

4

Start Page

63

End Page

80

Publisher

University of Isfahan

Peer Reviewed

1

Copyright

© 2013 University of Isfahan

Funder

This work is supported by Faculty Research Grant, Hong Kong Baptist University.

Link to Publisher's Edition

http://toc.ui.ac.ir/article_3678.html

ISSN (print)

22518657

ISSN (electronic)

22518665

Included in

Mathematics Commons

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