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Thu 29 Sep, 2005 03:59 pm
Hi,
I'm hoping that some one can help me with a problem I'm having.
The Question:
The line graph L(G) of a simple graph G is the graph whose vertices are in one-one correspondence with the edges of G, two vertices of L(G) being adjacent if and only if the corresponding edges of G are adjacent.
Show that the line graph of the tetrahedron is the octahedron (sorry, I don't know how to draw a picture of these on here.. just think of a tetrahedron with the points being vertices, same for the octahedron). I don't see how I can show this.. since there are more vertices in the octahedron than in the tetrahedron.. help!!
Hi, Sleepy....and welcome to A2K.
I'm sorry, but I haven't a clue as regards to solving your problem, but have replied to you so that your item appears at the top of the "at a glance" list again.
This will bring out the brainy people, and no doubt the solution or explanation will be forthcoming.
Good Luck.
Draw the tetrahedron in red. There are six edges.
Mark the midpoints of the six edges in blue.
If two red edges meet, draw a blue edge connecting their blue midpoints. Each midpoint will be connected to four other midpoints.
The final blue figure is the octahedron.
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