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1. Consider the graph G shown below. (a). The chromatic (vertex colouring number) is x(G) = (b). Explain briefly why x(G)- 1 colours are not enough: (c). Give a colouring using x(G) colours starting with A-1,B-2,C-3: B

1. Consider the graph G shown below. (a). The chromatic (vertex colouring number) is x(G) = (b). Explain briefly why x(G)- 1 colours are not enough: (c). Give a colouring using x(G) colours starting with A-1,B-2,C-3: B

Advanced Engineering Mathematics
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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1. Consider the graph G shown below. (a). The chromatic (vertex colouring number) is x(G) = (b). Explain briefly why x(G)- 1 colours are not enough: B (c). Give a colouring using x(G) colours starting with A-1,B-2,C-3: (d). Consider a graph G with x(G)- k, such that removing any vertex v from G decreases the chromatic number (G\v has chromatic number<k for all vertices u). We call such a graph colour critical. Is the graph above colour critical? Explain.
Transcribed Image Text:1. Consider the graph G shown below. (a). The chromatic (vertex colouring number) is x(G) = (b). Explain briefly why x(G)- 1 colours are not enough: B (c). Give a colouring using x(G) colours starting with A-1,B-2,C-3: (d). Consider a graph G with x(G)- k, such that removing any vertex v from G decreases the chromatic number (G\v has chromatic number<k for all vertices u). We call such a graph colour critical. Is the graph above colour critical? Explain.
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