Graphs Have at Least n-m Components | Graph Theory

Support the production of this course by joining Wrath of Math to access all my graph theory videos!    / @wrathofmath   🛍 Check out my math fashion brand! https://mathshion.com/ Graph Theory course:    • Graph Theory   Graph Theory exercises:    • Graph Theory Exercises   Get the textbook! https://amzn.to/3HvI535 A graph with n vertices and m edges has at least n-m components. We justify this claim in today's graph theory lesson. Imagine a graph with its n vertices and without any edges. This graph would have n components, each vertex is a trivial subgraph. Then, each additional edge could join at most two components, thus reducing the number of components by 1 at most. Hence, with m edges, the graph must have at least n-m components. #GraphTheory What is a Component of a Graph?    • What is a Component of a Graph? | Connecte...   ★DONATE★ ◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits:   / wrathofmathlessons   ◆ Donate on PayPal: https://www.paypal.me/wrathofmath Follow Wrath of Math on... ● Instagram:   / wrathofmathedu   ● Facebook:   / wrathofmath   ● Twitter:   / wrathofmathedu