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For the given graph with 10 vertices (as depicted), let's determine: 1. **Chromatic number ($$\chi(G)$$)**: the minimum number of colors to color the vertices so that no two adjacent vertices share the same color. 2. **Edge-chromatic number ($$\chi'(G)$$)**: the minimum number of colors needed to color the edges so that no two edges sharing a vertex have the same color. *** ## Chromatic Number ($$\chi(G)$$) To find the chromatic number: - Identify the size of the largest clique (complete subgraph). - Attempt to color the vertices while observing adjacencies. ### Observations: - Vertices $$v_1, v_5, v_6, v_8$$ _____ ____ _______ ____ ____ _________ ___.
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