The $ρ$-Capacity of a Graph

Sihuang Hu; Ofer Shayevitz

doi:10.1109/tit.2017.2669196

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arXiv · 1607.07263

The $ρ$-Capacity of a Graph

Sihuang Hu·Ofer Shayevitz

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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.

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Sihuang Hu, Ofer Shayevitz. 2017-02-09. The $ρ$-Capacity of a Graph. https://doi.org/10.1109/tit.2017.2669196

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