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. Extreme values of edge-friendly index of complete bipartite graphs will be determined.
Keywords
edge-friendly index, edge-friendly labeling, complete bipartite graph
Publication Date
2016
Source Publication Title
Transactions on Combinatorics
Volume
5
Issue
3
Start Page
11
End Page
21
Publisher
University of Isfahan
Peer Reviewed
1
Copyright
© 2016 University of Isfahan
Link to Publisher's Edition
http://toc.ui.ac.ir/article_12473_0.html
ISSN (print)
22518657
ISSN (electronic)
22518665
Recommended Citation
Shiu, Wai Chee. "Extreme edge-friendly indices of complete bipartite graphs." Transactions on Combinatorics 5.3 (2016): 11-21.