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7 cze 2024 · In this tutorial, we studied the conceptual bases of graph theory. We also familiarized ourselves with the definitions of graphs, vertices, edges, and paths. We’ve also studied the types of graphs that we can encounter and what are their predictable characteristics in terms of vertices, edges, and paths.
The connections between vertices are called edges. Represent an edge as a set fi, jg of two vertices. E.g., the edge between 2 and 5 is f2, 5g = f5, 2g. E = E(G) = set of edges = f1, 2g , f2, 3g , f2, 5g , f3, 4g , f3, 5g , f4, 5g Prof. Tesler Ch. 1. Intro to Graph Theory Math 154 / Winter 2020 4 / 42
V A graph is an ordered pair of sets (V, E) such that E is a subset of the set of unordered pairs of elements of V . The set V = V (G) is the set of vertices and E = E(G) is the set of edges. The vertices u and v are the endvertices of this edge and we also say that u, v are adjacent vertices in G.
Introduction to Graph Theory Loosely speaking, a graph is a collection of points called vertices and connecting segments called edges, each of which starts at a vertex, ends at a vertex and contains no other vertices
When we draw graphs, we think of the edges as connecting pairs of vertices, and represent edges by connecting their endpoints with curves. Below is the famous Petersen graph.
Based on class notes by Peter Maceli and Adrian Tang. A graph is a mathematical object we use to think about networks. It consists of a bunch of points, called vertices, and lines joining pairs of vertices, called edges. We usually let G denote the graph, V the set of vertices and E the set of edges, and write G = (V, E). adjacent otherwise.
