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hmw1.1 - Math 555 — Homework 1 1 Show that for any graph...

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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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