Quiz - MO412 - Matheus Rufino

Consider the following statements regarding planar multigraphs. Determine whether each statement is True (T) or False (F). 1. If a connected planar multigraph is bipartite, its total number of edges E  and vertices V  must strictly satisfy the inequality E <= 2V - 4  for all V >= 3 . 2. In any planar embedding of a connected multigraph, a bridge (cut-edge) in the primal graph corresponds to a self-loop in its geometric dual. 3. The sum of the degrees (lengths) of all faces in a planar embedding of a multigraph is exactly 2E , even if the graph contains self-loops or parallel edges. 4. Contracting any single edge in a non-planar multigraph will always yield a graph that is also non-planar. 5. A connected planar multigraph possesses an Eulerian circuit if and only if its geometric dual is a bipartite multigraph. 6. The Four Color Theorem guarantees that every planar multigraph can be properly vertex-colored using 4 or fewer colors. Which of the following sequenc...

 During the 2026 conflict in the Middle East, the Islamic Republic of Iran has closed the Strait of Hormuz. Applying network science to global supply chains during this geopolitical conflict is an excellent way to understand it`s real-world impact. Using Flow Network to understand why and how the flow of oil would be affected. Here is how the concept map to reality: Source Node(S): The oil fields where the resource originates (e.e., fields in Iran, Saudi Arabia, Venezuela, UAE, etc.) Sink Node(T): The global market or consumig nations (e.g., refineries in Asia, Eurpoe and the Americas) Intermidiete Nodes and Links: Export terminals, pumping stations and maritime transit chokepoints; shipping lanes and overland pipelines Capacities: Every edge has a maximum volume it can transport per day in millions of barrels per day. Based on the network flow model of the Global oil supply chain, with multiple source and sink nodes, which of the following statements is true? a) Assuming supp...

 A detective is searching for clues in a mansion and uses depth-first search(DFS) to investigate every room, he always moves to the next available door in alphabetical order. The mansion layout is: the Entrance has doors to the Ballroom and the Library. The Ballroom leads to the kitchen. The Kitchen leads to the Study and the Dining Room. The Library leads to the Observatory. The Dining Room, Study and Observatory don't lead to any relevant rooms. Which sequence correctly describes the detective's DFS walkthrough? a)   Entrance → Ballroom → Kitchen → Dining Room → Study → Library → Observatory b)  Entrance → Ballroom → Library → Kitchen → Dining Room → Study → Observatory c) Entrance → Ballroom → Kitchen → Dining Room → Library → Observatory → Study d)  Entrance → Library → Observatory → Ballroom → Kitchen → Dining Room → Study e) None of the above.

  A group of male friends wishes to elect a “group leader,” defined as the individual whom all others must follow for the day. Each friend casts exactly two vote for another member of the group. The election proceeds as follows: The individual receiving the highest number of votes is declared the winner. In the event of a tie, compare their clustering coefficients. The tied candidate with the smaller clustering coefficient is declared the winner, on the reasoning that if their supporters are not connected to one another, their “loyalty” is more securely independent. Although votes are inherently directed, the group mistakenly treated votes as a single undirected connection. Given the voting graph below, determine the winner of this entirely serious democratic exercise. The winner is: A. Don B. Bob C. Matt D. Neal E. None of the above