Let G be a simple undirected graph. Prove that (a) if G is disconnected, then d(GC) ≤ 2; (b) if d(G) > 3, then d(Gº) < 3; (c) if d(G) = 2 and A(G) = v - 2, then & > 2v - 4.

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter9: Systems Of Linear Equations
Section9.5: Multiplication With The Addition-or-subtraction Method
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Let G be a simple undirected graph. Prove that
(a) if G is disconnected, then d(GC) ≤ 2;
(b) if d(G) > 3, then d(Gº) < 3;
(c) if d(G) = 2 and A(G) = v - 2, then ɛ ≥ 2v - 4.
Transcribed Image Text:Let G be a simple undirected graph. Prove that (a) if G is disconnected, then d(GC) ≤ 2; (b) if d(G) > 3, then d(Gº) < 3; (c) if d(G) = 2 and A(G) = v - 2, then ɛ ≥ 2v - 4.
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