3. (a) (i) State the Handshaking Lemma. (ii) In each of the following cases, either draw a picture of the graph which matches the information, or explain why no such graph exists. • G1 with 4 vertices, each of degree 2; • G₂ with 5 vertices, each of degree 3; • G3 with 6 vertices, of which 2 of degree 1, 4 of degree 2; • G4 with 5 vertices, of which 1 of degree 1, 2 of degree 2, 2 of degree 4.
3. (a) (i) State the Handshaking Lemma. (ii) In each of the following cases, either draw a picture of the graph which matches the information, or explain why no such graph exists. • G1 with 4 vertices, each of degree 2; • G₂ with 5 vertices, each of degree 3; • G3 with 6 vertices, of which 2 of degree 1, 4 of degree 2; • G4 with 5 vertices, of which 1 of degree 1, 2 of degree 2, 2 of degree 4.
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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Transcribed Image Text:3. (a) (i) State the Handshaking Lemma.
(ii) In each of the following cases, either draw a picture of the graph which
matches the information, or explain why no such graph exists.
• G1 with 4 vertices, each of degree 2;
• G₂ with 5 vertices, each of degree 3;
·
G3 with 6 vertices, of which 2 of degree 1, 4 of degree 2;
• G with 5 vertices, of which 1 of degree 1, 2 of degree 2, 2 of degree
4.
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