b) Is the following graph isomorphic to Q4? If yes, give an isomorphism from Q4 to this graph. Otherwise, find a copy of Q3 in it. c) If v is a cut-vertex of a graph G, then v is also a cut-vertex of every induced subgraph of G containing v. Prove or disprove.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question

Please solve 2b and 2c

Give an example of each of the following:
a nonsimple plane graph with its dual a simple graph
a self-dual plane graph
iii)
i)
ii)
a plane graph whose each face is bounded by a triangle
iv)
a plane graph on 8 vertices with its dual having just one vertex
b)
Is the following graph isomorphic to Q4? If yes, give an isomorphism from Q4 to
this graph. Otherwise, find a copy of Q3 in it.
If v is a cut-vertex of a graph G, then v is also a cut-vertex of every induced
subgraph of G containing v. Prove or disprove.
с)
Transcribed Image Text:Give an example of each of the following: a nonsimple plane graph with its dual a simple graph a self-dual plane graph iii) i) ii) a plane graph whose each face is bounded by a triangle iv) a plane graph on 8 vertices with its dual having just one vertex b) Is the following graph isomorphic to Q4? If yes, give an isomorphism from Q4 to this graph. Otherwise, find a copy of Q3 in it. If v is a cut-vertex of a graph G, then v is also a cut-vertex of every induced subgraph of G containing v. Prove or disprove. с)
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