PTnet
Definitions – Graph Properties
20/3/2014
CE-653 - PTnet Theory and some
Algorithms
10
}Definition [Path]:
}A path of a net N=(S, T, F) is
an alternating sequence
π = (x0f0x1…fr-1xr) of elements X = S U T such that:
for all I, 0 ≤ i ≤ r – 1: fi = (xi, xi+1) in F
π = (x0f0x1…fr-1xr) of elements X = S U T such that:
for all I, 0 ≤ i ≤ r – 1: fi = (xi, xi+1) in F
}A path is elementary iff all xi are
distinct except x0 and xr
}A circuit is a path such that x0 = xr
}A circuit is elementary iff it is elementary as
a path
}Definition[Alternating Circuit]
}Let N = (S, T, F) be a
net. A circuit Γ of N (not necessarily elementary) is an alternating circuit iff for all arcs in Γ of the form (p, t) the equality
•t = {p} holds