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Number of neighbors of a set of vertices in a graph

Hi all, I'd like to know how to get the number of vertices that are adjacent to a given set of vertices in a graph. I have the following skeleton:

from sage.graphs.independent_sets import IndependentSets

G=[some graph]

J=IndependentSets(G)

And I would like to know the number of neighbors of x for each x in J (i.e., the number of vertices of G\x that are adjacent to some vertex in x). Ideally I would like something like:

F=0

t=var('t')

for x in J:

 N=number_of_neighbors(x)

F += t^N


F

If G is a four cycle then number_of_neighbors(x)=2 for any subset x of two vertices of G, and the polynomial F above should be 1+6t^2 (because there is the empty independent set, 4 independent sets of size 1 each with 2 neighbors, and 2 independent sets of size 2 each with 2 neighbors). I appreciate your help!

 2 None vdelecroix 6164 ●16 ●68 ●129 http://www.labri.fr/pe...

Number of neighbors of a set of vertices in a graph

Hi all, I'd like to know how to get the number of vertices that are adjacent to a given set of vertices in a graph. I have the following skeleton:

from sage.graphs.independent_sets import IndependentSets IndependentSets
G=[some graph] J=IndependentSets(G)graph]
J=IndependentSets(G)


And I would like to know the number of neighbors of x for each x in J (i.e., the number of vertices of G\x that are adjacent to some vertex in x). Ideally I would like something like:

F=0

t=var('t')

F=0
t=var('t')
for x in J:
N=number_of_neighbors(x)
for x in J:  N=number_of_neighbors(x)

F += t^N
F
F If G is a four cycle then number_of_neighbors(x)=2 for any subset x of two vertices of G, and the polynomial F above should be 1+6t^2 (because there is the empty independent set, 4 independent sets of size 1 each with 2 neighbors, and 2 independent sets of size 2 each with 2 neighbors). I appreciate your help! 


 3 retagged updated 2019-03-12 15:10:11 -0500 FrédéricC 2364 ●3 ●27 ●47 Number of neighbors of a set of vertices in a graph Hi all, I'd like to know how to get the number of vertices that are adjacent to a given set of vertices in a graph. I have the following skeleton: from sage.graphs.independent_sets import IndependentSets G=[some graph] J=IndependentSets(G) And I would like to know the number of neighbors of x for each x in J (i.e., the number of vertices of G\x that are adjacent to some vertex in x). Ideally I would like something like: F=0 t=var('t') for x in J: N=number_of_neighbors(x) F += t^N F If G is a four cycle then number_of_neighbors(x)=2 for any subset x of two vertices of G, and the polynomial F above should be 1+6t^2 (because there is the empty independent set, 4 independent sets of size 1 each with 2 neighbors, and 2 independent sets of size 2 each with 2 neighbors). I appreciate your help! 


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