S1.8- Algoritmo de Havel-Hakimi | 10/49 | UPV

Title: S1.8 - Havel-Hakimi Algorithm Self-description: This video covers the algorithm based on Havel and Hakimi's result to determine whether a sequence of non-negative integers is graphical, that is, whether it can represent the degrees of the vertices of a graph. The sequence must be ordered in decreasing order, and the theorem that states that a sequence is graphical if the sequence derived by subtracting one from the S subsequent numbers is also graphical is applied, repeating the process until lower or zero numbers are reached. It shows how to use the algorithm with a practical example: eliminate the largest number, subtract one from the following numbers, and reorder in decreasing order, connecting vertices in the graph according to these operations. This process is repeated until the numbers in the list are exhausted. Finally, the algorithm is used to design a computer network where the number of connections corresponds to the given sequence, verifying that it meets conditions such as the even degree sum lemma ("hand lemma"), and proceeding to construct the graph following the steps of the algorithm until the representation of the initial sequence is complete. Author: Conejero Casares José Alberto Course: This video is video 10/49 of the MOOC course Applications of Graph Theory to Real Life I | Universitat Politècnica de València UPV.    • MOOC Aplicaciones de la Teoría de Grafos a...   Polytechnic University of Valencia (UPV): https://www.upv.es More videos at:    / valenciaupv   Access our MOOCs: https://upvx.es #theory #graphs #mathematics #real #life #algorithm #havel-hakimi #mathematics