Egalitarian Edge Orderings of Complete Graphs

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


For a consecutive ordering of the edges of a graph G= (V, E) , the point sum of a vertex is the sum of the indices of edges incident with that vertex. Motivated by questions of balancing accesses in data placements in the presence of popularity rankings, an edge ordering is egalitarian when all point sums are equal, and almost egalitarian when two point sums differ by at most 1. It is established herein that complete graphs on n vertices admit an egalitarian edge ordering when n≡1,2,3(mod4) and n∉ { 3 , 5 } , or an almost egalitarian edge ordering when n≡0(mod4) and n≠ 4.

Original languageEnglish (US)
Pages (from-to)1405-1413
Number of pages9
JournalGraphs and Combinatorics
Issue number4
StatePublished - Jul 2021


  • Complete graph
  • Difference sum
  • Egalitarian block labelling
  • Supermagic labelling

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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