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$\begin{array}{|c|c|c|c|c|c|c|} \hline 0 & 1 & 1 & 0 & 1 & 1 & 0 \\ \hline 1 & 0 & 0 & 1 & 1 & 0 & 1 \\ \hline 1& 0 & 0 & 1 & 1 & 1 & 0 \\ \hline 0 & 1 & 1 & 0 & 1 & 0 & 1  \\ \hline 1 & 1 & 1 & 1 & 0 & 0 & 0 \\ \hline 1 & 0 & 1 & 0 & 0 & 0 & 1 \\ \hline 0 & 1 & 0 & 1 & 0 & 1 & 0 \\ \hline \end{array}$
Consider the above given adjacency matrix representation of a graph containing $7$ nodes (namely A , B, C, D, E, F, G). The Chromatic number of the given graph is?
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4 color theorem says that vertices of planar graph can be color at most 4 colors

and given graph is planar so it can be color with 4

be careful it is saying at most 4 , not 4 always
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@Gurdeep Saini

4 color theorem says that a planar graph can be colored with atmost 4 colors. Here we consider the fact of coloring the regions and not vertices. Isn't it?

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Ingraph-theoretic terminology, the four-color theorem states that the vertices of every planar graph can be colored with at most four colors so that no two adjacent vertices receive the same color, or for short, "every planar graph is four-colorable" https://en.wikipedia.org/wiki/Four_color_theorem

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1 Answer

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3 votes

Given graph is a planar graph . 

Answer:

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