Expected value expansions in rooted graphs

Authors:
Alison Bailey;Gary Gordon;Matthew Patton;Jennifer Scancella
Affiliations:
Mathematics Department, Lafayette College, Easton, PA;Mathematics Department, Lafayette College, Easton, PA;Mathematics Department, Lafayette College, Easton, PA;Mathematics Department, Lafayette College, Easton, PA
Venue:
Discrete Applied Mathematics
Year:
2003

Citing 13
Cited 1

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Abstract

When G is a rooted graph where each edge may independently succeed with probability p, we consider the expected number of vertices in the operational component of G containing the root. This expected value EV(G; p) is a polynomial in p. We present several distinct equivalent formulations of EV(G; p), unifying prior treatments of this topic. We use results on network resilience (introduced by Colbourn) to obtain complexity results for computing EV(G; p). We use some of these formulations to derive closed form expressions for EV(G; p) for some specific classes of graphs. We conclude by considering optimality questions for rooted graphs, root placement and some counterexamples.