GraphTheory
SpanningPolynomial
compute spanning polynomial
Calling Sequence
Parameters
Description
Examples
SpanningPolynomial(G, x)
G
-
undirected unweighted graph
x
variable or value
The SpanningPolynomial command returns a polynomial in x when x is a variable or the evaluation of the polynomial when x is a value. The value of this polynomial at a value 0≤p≤1 gives the probability that G is spanning (connected if G is connected) when each edge operates with probability p.
withGraphTheory:
withSpecialGraphs:
G≔PetersenGraph:
f≔SpanningPolynomialG,x
f≔704x15−4920x14+14430x13−22755x12+20370x11−9828x10+2000x9
evalf,x=0.75
0.8153727651
SpanningPolynomialG,0.35
0.02142980972
See Also
EdgeConnectivity
IsConnected
TuttePolynomial
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