The $\rho$-Capacity of a Graph

Abstract

Motivated by the problem of zero-error broadcasting, we introduce a new notion of graph capacity, termed $\rho$-capacity, that generalizes the Shannon capacity of a graph. We derive upper and lower bounds on the $\rho$-capacity of arbitrary graphs, and provide a Lovász-type upper bound for regular graphs. We study the behavior of the $\rho$-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 $\rho$-capacity.

arXiv comment21 pages

References in corpus (1)

• Simultaneous communication in noisy channels

Cited by in corpus (1)

• Variable-Length Coding for Zero-Error Channel Capacity