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- Show all work, graph, thank you!A graph whose vertices and edges can be drawn in a plane such that no two of the edges intersect.Let G be a simple connected plane graph with 6 vertices. (a) (b) (c) (d) What is the largest number of edges G can have? What is the least number of edges G can have? What is the largest number of faces G can have? Suppose that the numbers obtained in (a) & (c) are m & f respectively, construct a simple connected plane graph with 6 vertices, m edges and f faces.
- Construct a simple graph with vertices V, W, X, Y whose degrees are 1, 2, 0, 1 What is the edge set?Let G = (V, E) be a graph with vertex-set V = {1, 2, 3, 4, 5} and edge-setE = {(1, 2),(3, 2),(4, 3),(1, 4),(2, 4),(1, 3)}.(a) Draw the graph.Find (b) maximal degree, i.e. ∆(G),(c) minimal degree, i.e. δ(G),(d) the size of biggest clique, i.e. ω(G),(e) the size of biggest independent set, i.e. α(G), ter(f) the minimal number of colours needed to color the graph, i.e. χ(G).Consider the graph G with • V(G) = {2,3,6} • e(G) = {a, b, c, d, e, f, g} •E(G) = {(a, [2,2]), (b, [3,3]), (c, [6,6]), (d, [2,6]), (e, [6,2]), (f, [3,6]), (g, [6,3])} Using edge connectivity, we can define the relation R = {(2, 2), (3, 3), (6, 6), (2, 6), (6, 2), (3, 6), (6,3)} Which of the following statements are true? [More than one statement may be true.] R is reflexive. R is symmetric. R is transitive. R is antisymmetric.