1. For each of the graphs described below, either give an example of such a graph or explain why it does not exist. (a) A simple graph with 7 vertices with degrees 8, 5, 4, 4, 3, 1, 1 . (b) A simple graph with 8 vertices with degrees 4, 4, 4, 4, 4, 2, 2, 2. (c) A simple graph with 6 vertices with degrees 3, 3, 2, 2, 1, 1 that is a tree. (d) A simple graph with 8 vertices with degrees 3,3,2,2,1,1,1,1 that is a tree. (e) A simple graph with 6 vertices with degrees 4,4,3,3,2,1