Question $1$: Determine whether the undirected graphs shown have Euler circuits. Construct an Euler circuit if one exists. If no Euler circuit exists, determine whether the undirected graph has an Euler path. Construct an Euler path if one exists?

Question $2$: Use Dijkstra's algorithm to find the length of a shortest path between the following vertices in the weighted graph?

I. A and $F$

II$.$ A and D

III. B and $F$

Question $3$: Which of these nonplanar graphs have the property that the removal of any vertex and all edges incident with that vertex produces a planar graph?

a$)K_5$

b$)K_6$

c$)K_{3,3}$

d$)K_{3,4}$

Question $4$: Determine metric dimension$/$locating number of the graph G$.$

Question $5$: Find a route with the least total airfare that visits each of the cities in this graph, where the weight on an edge is the least price available for a flight between the two cities.