3. Describe whether the graph has an Euler circuit. If the graph has an Euler circuit, find one such circuit. 8 e10 es e14 e13 e12 e7 eг e15 9. e6 e11 (2) 3 ез ед es

Determine whether the graph has an Euler Circuit? Construct such a circuit when only one pathexits. If not an Euler circuit exists, determine whether the graph has an Euler path.

The line graph L(G) of a simple graph G is the graph whose vertices are in one-one correspondence with the edges of G, two vertices of L(G) being adjacent if and only if the corresponding edges of G are adjacent. Show that K3 and K, , have the same line graph. (i) (ii) Show that the line graph of the tetrahedron graph is the octahedron graph.

6) Consider the graph at the right: b. a. (5 pts) Does it have an Euler circuit? (5 pts) Does it have an Euler path? c. (5 pts) Does it have a Hamilton circuit? d. (5 pts) Does it have a Hamilton path? 1 2 4 K 6 7 9 10 11 12 3 13 00 8