Graph Theory FAQs: 01. More General Graph Definition

In video 02: Definition of a Graph, we defined a (simple) graph as a set of vertices together with a set of edges where the edges are 2-subsets of the vertex set. Notice that this definition does not allow for multiple edges or loops. In general on this channel, we have been discussing only simple graphs (no multiple edges or loops), so this definition is perfect for our needs (and is used in many textbooks and papers). However, if we require more precision in our definition of a graph, say if we want to consider loops or multiple edges, there is a standard general definition that we should use. It defines a graph as a set of vertices V, a set of edges E, and a mapping f which maps every edge to a set of endpoints. In this video we look at an example graph defined in this way and discuss how multiple edges and loops can come about. -- Bits of Graph Theory by Dr. Sarada Herke. Related videos: GT 02: Definition of a Graph - https://youtu.be/S1Zwhz-MhCs GT 09: Graph Isomorphisms - https://youtu.be/yFpRpxOry-A For quick videos about Math tips and useful facts, check out my other channel "Spoonful of Maths" - http://youtube.com/spoonfulofmaths