El concepto de grado en la teoría de grafos | 2/25 | UPV

Title: The Concept of Degree in Graph Theory Description: Definition of degree. Properties. Definition of in-degree and out-degree. Properties. Definition of a graph sequence and Hakimi's Theorem. Jordan Lluch, C. (2010). The Concept of Degree in Graph Theory. https://riunet.upv.es/handle/10251/7868 Automatic description: This video explains the concept of degree in graph theory, for both undirected and directed graphs, and introduces graph sequences. In undirected graphs, the degree of a vertex corresponds to the number of edges incident to it, counting loops as two. It highlights that the sum of the degrees of all vertices is equal to twice the number of edges and that the number of vertices with odd degree is even, derived from the sum of degrees. Graphical sequences consist of finite sequences of non-negative integers that represent the degrees of the vertices in a simple undirected graph. An example is given of how to determine if a sequence is graphical using previously mentioned properties, and Hakimi's theorem is introduced, which helps simplify this determination through an iterative process. On the other hand, in directed graphs, a distinction is made between in-degree and out-degree, since the edges, or arcs, have a defined direction. The in-degree (or out-degree) of a vertex is the number of arcs that terminate (or begin) at it. Furthermore, it is mentioned that the sum of the in-degrees is equal to the sum of the out-degrees and also to the total number of arcs in the directed graph. Finally, the video clarifies the terminology of "degree" specific to undirected and directed graphs, as well as the importance of specifying whether it refers to in-degree or out-degree in the latter case. Author: Cristina Jordan Lluch Course: This video is 2/42 of the course Basic Graph Theory and Analysis of 4 Well-Known Problems | Universitat Politècnica de València (UPV).    • Curso Teoría básica de grafos y análisis d...   Course: This video is 2/25 of the course Graph Theory. General Concepts...    • Teoría de Grafos. Conceptos Generales.   Universitat Politècnica de València (UPV): https://www.upv.es More videos at:    / valenciaupv   Access our MOOCs: https://upvx.es #Degree #Entry-level degree #Exit-level degree #APPLIED MATHEMATICS