Re: [sage-support] Re: bug in CirculantGraph(10,[2,4])?

[David Joyner]

On Mon, Jun 29, 2020 at 2:04 PM John H Palmieri 
wrote:

> According to wikipedia, graphs.CirculantGraph(n, [j_1, j_2, ...]) is
> connected if and only if gcd(n, j_1, j_2, ...) = 1. In this case, the gcd
> is 2. If Sage's definition is correct, it's defined as having 10 vertices,
> and vertex i is connected to vertices i+2, i-2, i+4, i-4, then even
> vertices will only be connected to other even vertices, so it should have
> two connected components.
>

Thanks! Sorry for the false alarm.


>
> (I'm not a graph theorist, and wikipedia is wikipedia, so take this with a
> grain of salt.)
>
>   John
>
>
> On Monday, June 29, 2020 at 10:25:26 AM UTC-7 wdjo...@gmail.com wrote:
>
>> Hi:
>>
>> In SageMath version 9.1.beta3, I get
>>
>> sage: Gamma1 = graphs.CirculantGraph(*10*,[*2*,*4*])
>>
>> sage: Gamma1.is_connected()
>>
>> False
>>
>>
>> My understanding is that all circulant graphs are connected.
>>
>> Is this a bug?
>>
>> - David
>>
>>
>>
>>
>> --
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> .
>

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[sage-support] Re: bug in CirculantGraph(10,[2,4])?

[John H Palmieri]

According to wikipedia, graphs.CirculantGraph(n, [j_1, j_2, ...]) is 
connected if and only if gcd(n, j_1, j_2, ...) = 1. In this case, the gcd 
is 2. If Sage's definition is correct, it's defined as having 10 vertices, 
and vertex i is connected to vertices i+2, i-2, i+4, i-4, then even 
vertices will only be connected to other even vertices, so it should have 
two connected components.

(I'm not a graph theorist, and wikipedia is wikipedia, so take this with a 
grain of salt.)

  John


On Monday, June 29, 2020 at 10:25:26 AM UTC-7 wdjo...@gmail.com wrote:

> Hi: 
>
> In SageMath version 9.1.beta3, I get
>
> sage: Gamma1 = graphs.CirculantGraph(*10*,[*2*,*4*])
>
> sage: Gamma1.is_connected()
>
> False
>
>
> My understanding is that all circulant graphs are connected. 
>
> Is this a bug?
>
> - David
>
>
>
>
>

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