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.

1 | initial version |

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.

~~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 |

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
```

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