Apply the greedy coloring algorithm with the order 1, 2, 3, ..., 7 to properly color the graph below. Determine the chromatic number and the independence number of this graph.
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We start with vertex 1 and assign it the first color (let's call it color A). Show more…
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Urvan J.
Being provided with the graph below: (i) Determine the chromatic polynomial alongside the chromatic number of the given graph. (ii) Provide a minimal proper coloring of that graph Additional Guideline: This question can be tackled using the known properties of chromatic polynomials. Can you regularly color it with 0, 1, 2 colors? Probably not, so it is p(G, ̀) = ̀(̀ - 1)(̀ - 2)(̀" + à + b) (5 nodes meaning degree 5, leading coefficient 1). Moreover, it must start like ̀⁵ - 8̀⁴ + ⋯ (8 edges), what can you conclude concerning the value of a? Have you tried to color it with 3 colors? Then, you must have found there are 6 ways to do that, and p(G,3)=6 gives you the value of b.
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Construct a coloring of the graph shown using this algorithm.
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