a) What is graph coloring & Chromatic number. Find out the chromatic number for the following graph. NT WA SA V T NSW b) Write down the difference between walk & path. Find out the minimum spanning tree using Kruskal Algorithm for the following graph 1 5 6 1 2 5 4 5 2 3 3 6 4 5 6 6
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The chromatic number of a graph is the minimum number of colors needed to color the graph. To find the chromatic number for a graph, we need to determine the minimum number of colors required to color the graph such that no two adjacent vertices have the same Show more…
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Find the chromatic number of each of the following graphs: (i) C7 (the cycle on 7 vertices), (ii) C8, (iii) a bipartite graph with at least one edge, (iv) a tree with n > 1 vertices
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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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