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...