Unformatted text preview: Math. 555 — Homework # 1 1) Show that for any graph I‘
oﬂ‘) — e(I‘) i: 1 with equality holding HT 1" is a tree, where oﬂ‘}, e(I‘) denote
the number of yertices. edges respectively. 2) Let P be a regular polygon in which each face has 3.3 edges
and for which q faces meet at each vertex. Using Euler's formula
prove that 1+1
2 e. I
+
I
II 3) Use the preceding result to show that there are only ﬁve regular
polyhedra. 1) Use Euler's formula to compute the number of faces, edges
and yertices in the following polyhedra: ...
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 Spring '08
 Ogle,C
 Topology

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