Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

Abstract

‎‎Let G=(V,E)G=(V,E) be a simple graph‎. ‎An edge labeling f:E→{0,1}f:E→{0,1} induces a vertex labeling f+:V→\Z2f+:V→\Z2 defined by f+(v)≡∑uv∈Ef(uv)(mod2)f+(v)≡∑uv∈Ef(uv)(mod2) for each v∈Vv∈V‎, ‎where \Z2={0,1}\Z2={0,1} is the additive group of order 2‎. ‎For i∈{0,1}i∈{0,1}‎, ‎let‎ ‎ef(i)=|f−1(i)|ef(i)=|f−1(i)| and vf(i)=|(f+)−1(i)|vf(i)=|(f+)−1(i)|‎. ‎A labeling ff is called edge-friendly if‎ ‎|ef(1)−ef(0)|≤1|ef(1)−ef(0)|≤1‎. ‎If(G)=vf(1)−vf(0)If(G)=vf(1)−vf(0) is called the edge-friendly index of GG under an edge-friendly labeling ff‎. ‎The full edge-friendly index set of a graph GG is the set of all possible edge-friendly indices of GG‎. ‎Full edge-friendly index sets of complete bipartite graphs will be determined‎.

Keywords

Full edge-friendly index sets‎, ‎edge-friendly index‎, ‎edge-friendly labeling‎, ‎complete bipartite graph

Publication Date

6-2017

Source Publication Title

Transactions on Combinatories

Volume

6

Issue

2

Start Page

7

End Page

17

Publisher

University of Isfahan

Peer Reviewed

1

Copyright

© 2017 University of Isfahan

DOI

10.22108/TOC.2017.20739

Link to Publisher's Edition

http://dx.doi.org/10.22108/TOC.2017.20739

ISSN (print)

22518657

ISSN (electronic)

22518665

Included in

Mathematics Commons

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