Mixing
Graphs theory chromatic polynomial
$begingroup$
graph G I have this graph, I found their chormatic polynomial
$P_G (k)=k(k-1) (k^2-3k+3)^2,$ It's right?
My question is how I determine the number of proper colourings of K3 + G with 5 colours, Can i add it like a simple polinomio? and replace k=5?
K3(complete graph) + G (image add) is related with join of graphs.
The join K3+G is the graph that has the vertices and the edges of the original graphs, in addition to the edges that connect all the vertices of K3 with all the vertices of G.
But I could not get the chromatic polynomial.
Thanks for your help.
graph-theory
asked Jan 13 at 22:24
FerFer
32
$endgroup$
add a comment |
$begingroup$
graph G I have this graph, I found their chormatic polynomial
$P_G (k)=k(k-1) (k^2-3k+3)^2,$ It's right?
My question is how I determine the number of proper colourings of K3 + G with 5 colours, Can i add it like a simple polinomio? and replace k=5?
K3(complete graph) + G (image add) is related with join of graphs.
The join K3+G is the graph that has the vertices and the edges of the original graphs, in addition to the edges that connect all the vertices of K3 with all the vertices of G.
But I could not get the chromatic polynomial.
Thanks for your help.
graph-theory
asked Jan 13 at 22:24
FerFer
32
$endgroup$
2
$begingroup$
Sorry, I don't know what is meant by K3+G.
$endgroup$
– saulspatz
Jan 13 at 22:32
$begingroup$
Hi, sorry about it, it is related with join of graphs and the chormatic polynomial of it
$endgroup$
– Fer
Jan 14 at 21:23
$begingroup$
@saulspatz Hi, sorry about it, it is related with join of graphs and the chormatic polynomial of it G1 + G2 = (V1 [ V2; (E1 [ E2 [ ffu; vg j u 2 V1; v 2 V2g)):
$endgroup$
– Fer
Jan 15 at 1:41
add a comment |
$begingroup$
graph G I have this graph, I found their chormatic polynomial
$P_G (k)=k(k-1) (k^2-3k+3)^2,$ It's right?
My question is how I determine the number of proper colourings of K3 + G with 5 colours, Can i add it like a simple polinomio? and replace k=5?
K3(complete graph) + G (image add) is related with join of graphs.
The join K3+G is the graph that has the vertices and the edges of the original graphs, in addition to the edges that connect all the vertices of K3 with all the vertices of G.
But I could not get the chromatic polynomial.
Thanks for your help.
graph-theory
asked Jan 13 at 22:24
FerFer
32
$endgroup$
graph G I have this graph, I found their chormatic polynomial
$P_G (k)=k(k-1) (k^2-3k+3)^2,$ It's right?
My question is how I determine the number of proper colourings of K3 + G with 5 colours, Can i add it like a simple polinomio? and replace k=5?
K3(complete graph) + G (image add) is related with join of graphs.
The join K3+G is the graph that has the vertices and the edges of the original graphs, in addition to the edges that connect all the vertices of K3 with all the vertices of G.
But I could not get the chromatic polynomial.
Thanks for your help.
graph-theory
graph-theory
asked Jan 13 at 22:24
FerFer
32
asked Jan 13 at 22:24
FerFer
32
edited Jan 16 at 1:18
Fer
asked Jan 13 at 22:24
FerFer
32
asked Jan 13 at 22:24
FerFer
32
asked Jan 13 at 22:24
FerFer
32
32
2
$begingroup$
Sorry, I don't know what is meant by K3+G.
$endgroup$
– saulspatz
Jan 13 at 22:32
$begingroup$
Hi, sorry about it, it is related with join of graphs and the chormatic polynomial of it
$endgroup$
– Fer
Jan 14 at 21:23
$begingroup$
@saulspatz Hi, sorry about it, it is related with join of graphs and the chormatic polynomial of it G1 + G2 = (V1 [ V2; (E1 [ E2 [ ffu; vg j u 2 V1; v 2 V2g)):
$endgroup$
– Fer
Jan 15 at 1:41
add a comment |
2
$begingroup$
Sorry, I don't know what is meant by K3+G.
$endgroup$
– saulspatz
Jan 13 at 22:32
$begingroup$
Hi, sorry about it, it is related with join of graphs and the chormatic polynomial of it
$endgroup$
– Fer
Jan 14 at 21:23
$begingroup$
@saulspatz Hi, sorry about it, it is related with join of graphs and the chormatic polynomial of it G1 + G2 = (V1 [ V2; (E1 [ E2 [ ffu; vg j u 2 V1; v 2 V2g)):
$endgroup$
– Fer
Jan 15 at 1:41
2
2
$begingroup$
Sorry, I don't know what is meant by K3+G.
$endgroup$
– saulspatz
Jan 13 at 22:32
$begingroup$
Sorry, I don't know what is meant by K3+G.
$endgroup$
– saulspatz
Jan 13 at 22:32
$begingroup$
Hi, sorry about it, it is related with join of graphs and the chormatic polynomial of it
$endgroup$
– Fer
Jan 14 at 21:23
$begingroup$
Hi, sorry about it, it is related with join of graphs and the chormatic polynomial of it
$endgroup$
– Fer
Jan 14 at 21:23
$begingroup$
@saulspatz Hi, sorry about it, it is related with join of graphs and the chormatic polynomial of it G1 + G2 = (V1 [ V2; (E1 [ E2 [ ffu; vg j u 2 V1; v 2 V2g)):
$endgroup$
– Fer
Jan 15 at 1:41
$begingroup$
@saulspatz Hi, sorry about it, it is related with join of graphs and the chormatic polynomial of it G1 + G2 = (V1 [ V2; (E1 [ E2 [ ffu; vg j u 2 V1; v 2 V2g)):
$endgroup$
– Fer
Jan 15 at 1:41
add a comment |
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$begingroup$
Sorry, I don't know what is meant by K3+G.
$endgroup$
– saulspatz
Jan 13 at 22:32
$begingroup$
Hi, sorry about it, it is related with join of graphs and the chormatic polynomial of it
$endgroup$
– Fer
Jan 14 at 21:23
$begingroup$
@saulspatz Hi, sorry about it, it is related with join of graphs and the chormatic polynomial of it G1 + G2 = (V1 [ V2; (E1 [ E2 [ ffu; vg j u 2 V1; v 2 V2g)):
$endgroup$
– Fer
Jan 15 at 1:41