QUESTION:
Suppose that a connected planer simple graph has 25 edges. If a plane drawing of this graph has 10 faces, how many vertices does this graph have?
QUESTION:
Suppose that a connected planer simple graph has 25 edges. If a plane drawing of this graph has 10 faces, how many vertices does this graph have?
Such a graph satisfies Euler's Polyhedron formula:
n-m+f=2
where n is the number of vertices, m the number of edges, and f the
number of faces. So:
Is this just pretty much the same as Euler's Relationship:
R + N = A + 2 ?
I am not sure what you are saying but there is:
1)Euler Formula for Planar Graphs.
2)Euler Formula for Polyhedra.
These two formulas are the same.
#1 is stronger than #2.
Because I believe one way of proving #2 is from #1.
Such a graph satisfies Euler's Polyhedron formula:
n-m+f=2
where n is the number of vertices, m the number of edges, and f the
number of faces. So:
n=2+25-10=17.
RonL
is there a way of finding the number of faces (or regions as its called in our classnotes) from just looking at a graph? eg. how many faces/regions does $\displaystyle K_{3,3}$ have?