Question

Most Edges. Prove that if a graph with n vertices has chromatic number n, then the graph has n(n-1) edges. Divide. Let V = {1, 2, ..., 10} and E = {(x, y) : x, y € V, x + y, , and a divides y}. Draw the directed graph with vertices V and directed edges E.

Answer 1

given that graph has n vertices, so, each vertex is adjacent to every other one and the degree of each vertex is - Now by Hand-shake Lemma I degree) = 216 VEV Here v is the vertex set and Eis the Edge set. (n-1) +(n-1) + ----(n-1) 2시티 netimes non-1) = 21E) -> TEI= Inan-1) 2 Hence graph has 1 (1-1) Edges.

a Qus given 1= 1,2,3,4,5,6,7,8,9,105 E = {(xit) | x,y EV, XEY,& divides y} E={(1,2),(1,3), (1,4),(1,5),(1,6),(47),(1,8),(1,9) (1,10),(2,4),(2,6),(2,8), (2,10),(3,6),(3,9) (4,8),(5, (5, 10) { 2 lo 3 9 4 7 6
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