The ρ-Capacity of a Graph

Sihuang Hu, Ofer Shayevitz

Research output: Contribution to journalArticlepeer-review

Abstract

Motivated by the problem of zero-error broadcasting, we introduce a new notion of graph capacity, termed ρ-capacity, that generalizes the Shannon capacity of a graph. We derive upper and lower bounds on the ρ-capacity of arbitrary graphs, and provide a Lovász-type upper bound for regular graphs. We study the behavior of the ρ-capacity under two graph operations: the strong product and the disjoint union. Finally, we investigate the connection between the structure of a graph and its ρ-capacity.

Original languageEnglish
Article number7855818
Pages (from-to)2241-2253
Number of pages13
JournalIEEE Transactions on Information Theory
Volume63
Issue number4
DOIs
StatePublished - Apr 2017

Keywords

  • Shannon capacity of a graph
  • Zero-error broadcasting
  • ρ-capacity

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