Let G be a simple graph that has 10 vertices and 38 edges. Prove thatG contains K4 (the complete graph on four vertices) as an inducedsubgraph.(6) Let G be a simple graph in which all vertices have degree four. Provethat it is possible to color the edges of G orange or blue so that eachvertex is adjacent to two orange edges and two blue edges.(7) How many different simple graphs are there on the vertex set [n]?(8) An automorphism of a graph G is an isomorphism between G and Gitself. That is, the

1 the graph g has 6 vertices with degrees 223445 how many edges does g have 2 a connected graph g has 10 vertices with which of the following extra conditions g must be a tree a g has at lea 33976

Draw a graph with 10 vertices. Label each vertex with one of th... | Filo