3. [ 30 points ] The graph shown is K4 : a b (a) Does this graph have an Euler circuit? If so, what is it? If not, why n

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3 30 Points The Graph Shown Is K4 A B A Does This Graph Have An Euler Circuit If So What Is It If Not Why N 1 (135.47 KiB) Viewed 29 times

3. [ 30 points ] The graph shown is K4 : a b (a) Does this graph have an Euler circuit? If so, what is it? If not, why not? (b) Does this graph have an Euler path? If so, what is it? If not, why not? (c) Does this graph have a Hamilton circuit? If so, what is it? If not, why not? (d) Verify that K4 is planar by re-drawing the graph so that no edges cross. (e) Use your graph in part (d) to verify “Euler's formula” : (# of edges ) -(# of vertices ) + 2 = (total # of regions, including outer region)