2) Parts (a) and (b) on this page are separate.(a) An undirected simple graph has 1000 vertices of degree 6 and 200 vertices of de-gree 2. This accounts for all vertices. How many edges does it have?Work this out to a final numeric answer.(b) How many directed simple graphs (no loops or multiple edges) are there on vertexset {0, 1,...,9}?Express your answer to (b) using an appropriate formula with specific numbersplugged in, such as V100! + 2, rather than evaluating it to a final numerical result.

Answered: (a) An undirected simple graph has 1000…

(a) An undirected simple graph has 1000 vertices of degree 6 and 200 vertices of de- gree 2. This accounts for all vertices. How many edges does it have? Work this out to a final numeric answer.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

2) Parts (a) and (b) on this page are separate.
(a) An undirected simple graph has 1000 vertices of degree 6 and 200 vertices of de-
gree 2. This accounts for all vertices. How many edges does it have?
Work this out to a final numeric answer.
(b) How many directed simple graphs (no loops or multiple edges) are there on vertex
set {0, 1,...,9}?
Express your answer to (b) using an appropriate formula with specific numbers
plugged in, such as V100! + 2, rather than evaluating it to a final numerical result.

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