filmov
tv
Graph theory: Video 018. Induced subgraph and Underlying simple subgraph
![preview_player](https://i.ytimg.com/vi/lLiqAXl9uP8/sddefault.jpg)
Показать описание
Mathematics, Graph theory. Induced subgraph and Underlying simple subgraph In the mathematical field of graph theory, an induced subgraph of a graph is another graph, formed from a subset of the vertices of the graph and all of the edges (from the original graph) connecting pairs of vertices in that subset. Definition of induced subgraph: Formally, let G(V,E) be any graph, and let S, V be any subset of vertices of G. Then the induced subgraph G[S] is the graph whose vertex set is S and whose edge set consists of all of the edges in E that have both endpoints in G .That is, for any two vertices , and are adjacent in if and only if they are adjacent in . The same definition works for undirected graphs, directed graphs, and even multigraphs. The induced subgraph may also be called the subgraph induced in by , or (if context makes the choice of unambiguous) the induced subgraph of G. Mark: Every induced subgraph is also an ordinary subgraph, but not conversely. underlying simple graphofG. Definition. Given spanning subgraphsF1 = (V, E1) andF2 = (V, E2) of a graphG= (V, E), we form the spanning subgraph ofGwhose edge set is the symmetricdifferenceE14E2 = (E1E2)∪(E2E1). This graph is thesymmetric differenceof graphsF1 andF2, denotedF14F2. In this video, you will learn about the induced subgraph: what is induced subgraph, and some examples about induced subgraph and also underlying simple graph. I'm Assistant prof. Abdultamim Ahadi, PhD scholar at University of Kerala, lecturer at Mathematics department and former Vice Chancellor for Students Affairs of Al-Beruni University. I usually post 2-4 new videos each week, so if you're interested to learning mathematics step by step, make sure to subscribe and turn on notifications so that you see all of my new videos.
Комментарии