Full edge-friendly index sets of complete bipartite graphs

Wai Chee Shiu

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)7-17
JournalTransactions on Combinatorics
Volume6
Issue number2
DOIs
Publication statusPublished - Jun 2017

User-Defined Keywords

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

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