On the st-spread resistance of a graph
Let G = (V, E) be an undirected nontrivial loopless graph with possible parallel edges. We presuppose that the vertex s in G is labelled at initial lime step and that every labelled vertex spreads its labelling to neighbouring vertices with infection probability p in one time step. In this paper, we...
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| Format: | text |
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Animo Repository
2010
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| Online Access: | https://animorepository.dlsu.edu.ph/faculty_research/7816 |
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| Institution: | De La Salle University |
| Summary: | Let G = (V, E) be an undirected nontrivial loopless graph with possible parallel edges. We presuppose that the vertex s in G is labelled at initial lime step and that every labelled vertex spreads its labelling to neighbouring vertices with infection probability p in one time step. In this paper, we deal with special case of this spread process called st-spread resistance of G, defined as
Pst(G) = lim p • Tst(G),p→0
where Tst ( G) is the expected first arrival time the spread process reaches the target vertex t from s in G. Moreover, we find a recurrence equation for Pst( G) and establish the connection between Pst(G) to the Kulkami 's exponential spreading model where the waiting time assigned to each edge in G is an exponential random variate intensity p. |
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