Draw all nonisomorphic simple graphs with four vertices and no more than two edges.

A school consists of 6 separate buildings, represented by the vertices in the graph. There are paths between some of the buildings as shown. The graph also shows the length in feet of each path. School administrators want to cover some of these paths with roofs so that students will be able to walk between buildings without getting wet when it rains. To minimize cost, they must select paths to be covered such that the total length to be covered is as small as possible. Use Kruskal's algorithm to determine which paths to cover. Also determine the total length of pathways to be covered. OA. Click here to view figure c. OC. Click here to view figure b. A The total length of pathways to be covered is (Type a whole number.) 45 B Find a minimum spanning tree. Choose the correct answer below. 51 34 19 39 25 E 31 29 30 25 F41 (... D 35 O B. Click here to view figure d. O D. Click here to view figure a.

All cycle graphs are also K-regular graphs. True or False

Let P₁ and P₂ be two paths of maximum length in a connected graph G. Prove that P₁ and P2 have a common vertex.