Word Count : 487

---

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 $$v_1, v_5, v_6, v_8$$ seem to form a cycle with additional interconnections. - Vertex $$v_5$$ is a high-degree vertex, connected to $$v_4, v_6, v_9, v_{10}$$, etc. - There ______ ________ _____ ________ ___ __________ ________ ____ ________.
______ ___ ____ _______ _____.
_______ _______ _________ ______ ____ _________ ______ __________ _________.
__________ ______ ___ ________ ________ ________ ___.
___ ___ _______ _________ ________ _____ __________ ___ _____ ________ __________.
____ ____ __________ _________ ________ ___.
_____ ____ __________ _______ _____ _________ ______ __________ __________.
________ ________ _____ ____ _____ ____ _____ ___ _____ _____ ________ _________.
_______ ______ _______ __________ ________ _____ ___ _____ ________.
_____ ___ __________ ____ ___ ___ ______.
_______ _________ ______ ___ ____ ____ _______ ________ _____.
________ ________ ______ ______ ____ _______ __________ _______ _______.
________ ______ ____ _________ _______ _______.
_____ ____ ________ ________ ________ __________ ____ ___ _____.
_________ _____ _____ _________ _____ ________.
__________ _________ _____ __________ _____ __________ _______ _______ ___.
___ ___ __________ ___ ____ _________ ___ _________ ____ ____ ________ __________.
______ __________ _________ _______ _______ _____.
______ _____ _____ _______ ___ ______ ____ __________ ___ __________ __________.
__________ __________ _______ _________ ________ ______.
__________ __________ ___ _____ _____ ______ _____ __________ _____ _______.
__________ ____ ___ _______ ___ __________ _________ _________ __________.
__________ _________ __________ __________ __________ ________ __________ ___ _____ _____ ______.
_____ ____ ___ __________ _______ ______ ___ ____ ____ ________.
_______ ________ _______ _____ _______ _______ __________ ______ ________.
_____ __________ _________ ___ _____ ______ __________ __________ _______ ____ __________ ____.
___ __________ __________ ________ ___ ___ _____ ______ ______ _____ _________.
_____ ___ _______ _____ ________ _________ ___.
_____ _____ _________ ________ ____ ______ ________ ____ _________.
_____ __________ ______ ____ _________ ____.
________ ___ ____ _________ ____.
_______ _____ ______ __________ ______ _________ __________ ____ _________ _____ ____.
___ ___ ____ __________ __________.
_________ _____ _____ _____ ________ _________ ____ _______ _______ _____ ________ ____.
__________ _________ ______ _________ ____ ________ _______ ________ _____.
______ _________ _________ _____ ______ ________ ____ ______ _________ _________.
______ ___ ____ ___ _____ ___.
___ _______ _______ ___ _______ _____ _________ ____ _________ ___.
________ ___ __________ ______ __________ _______ __________ ________ _____ ____ ______.
__________ _____ _____ ________ __________ _______ _________ _____ ___ _________ ___.
________ __________ _____ _________ ______ ________ _________ ______ _______ ____ _____ _____.
____ ___ ______.
Get Full Answer on WhatsApp