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help please :$

how do i go about doing these?

not sure if what i've done is correct..very stuck with the last question especially..
please help :colondollar:
(edited 13 years ago)
Original post by Minni04

not sure if what i've done is correct.


Neither am I, since you've not posted any working.

PS. A more descriptive title would help, since I couldn't tell it was graph theory until I opened the attachment.
(edited 13 years ago)
Reply 2
OK WELL ooops sorry
yeh well the answers for question 1 i got are:

c,f,g,i
b,e,j,k
a,d,h,l


b) 3,2,2,2
3,3,2,2
3,3,2,2

c)b,e,j,k is isomorphic to a,d,h,i
Map: h->e, a->b,l->j, d->k

1d) 0 because b and l are disconnected
Reply 3
Original post by Minni04
OK WELL ooops sorry
yeh well the answers for question 1 i got are:

c,f,g,i
b,e,j,k
a,d,h,l


b) 3,2,2,2
3,3,2,2
3,3,2,2

c)b,e,j,k is isomorphic to a,d,h,i
Map: h->e, a->b,l->j, d->k

1d) 0 because b and l are disconnected


It's Ok for me
For 1d: it will be strictly correct if
you write dow the adjacency matrix (A) and
multiply it by itself 5 times -> A5A^5
Where Aij5=1A^5_{ij}=1 there exists a walk of 5 length
from i vertex to j vertex.
Original post by Minni04
OK WELL ooops sorry
yeh well the answers for question 1 i got are:

c,f,g,i
b,e,j,k
a,d,h,l


Agreed.


b) 3,2,2,2
3,3,2,2
3,3,2,2


Disagree with your first one. The degree of both f and g is 3, and the other two are 2, so you have the same degree sequence as the other two connected components.

It is a convention that a loop contributes "2" to the degree of a vertex, although it is only one edge.


c)b,e,j,k is isomorphic to a,d,h,i
Map: h->e, a->b,l->j, d->k


Yep, that's one. Additionally, drawing the two side by side with identical shape would be good "evidence" to support your assertion.

Or if you're familiar with adjacency matrices, which ztibor has mentioned, showing that they have the same adjacency matrix with suitably arranged vertices would give you the algebraic evidence.


1d) 0 because b and l are disconnected


Yes, they are in different connected components.
(edited 13 years ago)

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