(a) (C) (d) (8) Draw a graph G with all of the following properties. G has six vertices. G has eight edges. Three vertices of G have degree two. Two vertices of G have degree three. One vertex of G' has degree four. Make sure your drawing is decently large (roughly three inches by three inches). N otes / Advice: It may help to think about what. vertices of degree two, three, and four look like before trying to form the full graph. There are multiple graphs that. have the list of properties above, so don't. worry about hunting for only one special graph out there. Build a strategy by making mistakes and learning from them. If you make a graph that doesn't. work, figure out why it doesn't. work and try to make a modification. Note that edges of a graph are allowed to be curved and are allowed to cross over each other. Redraw your graph G from part (a). Make sure your drawing is decently large (roughly three inches by three inches). Label each vertex of G with its degree. Use a theorem to state why G does NOT contain an Euler circuit. Redraw your graph G from part (a). Make sure your drawing is decently large (roughly three inches by three inches). Label each vertex of G with its degree. Use a theorem to state why G contains an Euler path. Provide an example of such a path by circling the starting vertex, circling the ending vertex, and lettering the edges (using A, B, C, D, E, F, G, and H) in the order that you walk over them. Redraw your graph G' from part (a). Make sure your drawing is decently large (roughly three inches by three inches). Add a new edge between two vertices of G so that you create a new graph that DOES contain an Euler circuit. Provide an example of such a circuit by circling the starting/ending vertex and lettering the edges (using A, B, C, D, E, F, G, H, and I) in the order that you walk over them. Suppose the vertices of G represent. a group of people and each edge of G represents friendship between two people. In this context, what information does the degree of a vert ex provide?la) (b) (d) (e) Suppose the vertices of G represent a gro Draw a graph G with all of the following properties. G has six vertices. G has eight edges. Three vertices of G have degree two. Two vertices of G have degree three. One vertex of G has degree four. Make sure your drawing is decently large (roughly three inches by three inches). Notes / Advice: It may help to think about what vertices of degree two, three, and four look like before trying to form the full graph. There are multiple graphs that have the list of properties above, so don't worry about hunting for only one special graph out there. Build a strategy by making mistakes and learning from them. If you make a graph that doesn't work, figure out why it doesn't work and try to make a modification. Note that edges of a graph are allowed to be curved and are allowed to cross over each other. Redraw your graph G from part (a). Make sure your drawing is decently large (roughly three inches by three inches). Label each vertex of G With its degree. Use a theorem to state why G does NOT contain an Euler circuit. G from part (a). Make sure your drawing is decently large (roughly ' es). Label each vertex of G with its degree. Use a theorem Euler path. Provide an example of such a path by circling ing vertex, and lettering the edges (using A, B, C, D, E, F, G, and H) in the order that you walk over them. Redraw your graph G from part (a). Make sure your drawing is decently large (roughly three inches by three inches). Add a new edge between two vertices of G so that graph that DOES contain an Euler circuit. Provide an example of 'ng/ ending vertex and lettering the edges (using A, d I) in the order that you walk over them. up of people and each edge of G represents friendship between two people. In this context, What information does the degree of a vertex provide