On the st-spread resistance of a graph

• Main Author: Lapus, Raymond R.
• Format: text
• Published: Animo Repository 2010
• Subjects: Graph theory; Mathematics
• Online Access: https://animorepository.dlsu.edu.ph/faculty_research/7816
• Institution: De La Salle University

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.