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### chromatic polynomial graph with loops

In Sage v8.6, the output of the function:

Graph([[1,1]],multiedges=True,loops=True).chromatic_polynomial()

is:

x

but it seems to me that, if graphs with loops are allowed, it should be:

0

as there are no proper colorings of graphs with loops.

 2 None slelievre 15399 ●18 ●144 ●304 http://carva.org/samue...

### chromatic polynomial graph with loops

In Sage v8.6, the output of the function:

Graph([[1,1]],multiedges=True,loops=True).chromatic_polynomial()

is:

x

but it seems to me that, if graphs with loops are allowed, it should be:

0

as Since there are no proper colorings of graphs with loops. loops, their chromatic polynomial should be zero.

SageMath 8.6 however seems to ignore the loops and returns a nonzero chromatic polynomial for the graph on one vertex with one loop edge.

sage: Graph([[1, 1]], multiedges=True, loops=True).chromatic_polynomial()
x
 3 retagged slelievre 15399 ●18 ●144 ●304 http://carva.org/samue...

### chromatic polynomial graph with loops

Since there are no proper colorings of graphs with loops, their chromatic polynomial should be zero.

SageMath 8.6 however seems to ignore the loops and returns a nonzero chromatic polynomial for the graph on one vertex with one loop edge.

sage: Graph([[1, 1]], multiedges=True, loops=True).chromatic_polynomial()
x