Expected rank and randomness in rooted graphs

Authors:
David Eisenstat;Jennifer Feder;Greg Francos;Gary Gordon;Amanda Redlich
Affiliations:
Department of Computer Science Princeton University, 35 Olden Street, Princeton, NJ 08540, USA;Department of Biostatistics, Johns Hopkins University, Baltimore, MD 21205, USA;Department of Mathematics, 301 Thackeray Hall University of Pittsburgh, Pittsburgh, PA 15260, USA;Department of Mathematics, Lafayette College, Easton, PA 18042, USA;Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139, USA
Venue:
Discrete Applied Mathematics
Year:
2008

Citing 5
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Abstract

For a rooted graph G, let EV"b(G;p) be the expected number of vertices reachable from the root when each edge has an independent probability p of operating successfully. We determine the expected value of EV"b(G;p) for random trees, and include a connection to unrooted trees. We also consider rooted digraphs, computing the expected value of a random orientation of a rooted graph G in terms of EV"b(G;p). We consider optimal location of the root vertex for the class of grid graphs, and we also briefly discuss a polynomial that incorporates vertex failure.