Connectivity (graph theory) - Wikipedia
In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to …
Connected Graph -- from Wolfram MathWorld
4 天之前 · A connected graph is graph that is connected in the sense of a topological space, i.e., there is a path from any point to any other point in the graph. A graph that is not connected is …
5.1: The Basics of Graph Theory - Mathematics LibreTexts
If a graph \(G\) is not connected, define \(v\sim w\) if and only if there is a path connecting \(v\) and \(w\). It is not hard to see that this is an equivalence relation. Each equivalence class …
connected component (or CC) of G is a maximal set of mutually reachable nodes. Here’s a collection of useful facts about graphs that you can take as a given. a path from u to v if and …
A connected graph is a tree if and only if it has n 1 edges. I. In a tree, there is a unique path between any two nodes. I. A forest is a graph in which each component is a tree. I. A star is a …
5.7: Connectivity - Mathematics LibreTexts
If a graph \(G\) is connected, any set of edges whose removal disconnects the graph is called a cut. \(G\) has edge connectivity \(k\) if there is a cut of size \(k\) but no smaller cut; the edge …
k-Connected Graph -- from Wolfram MathWorld
2025年1月14日 · A graph on more than two vertices is said to be -connected (or -vertex connected, or -point connected) if there does not exist a vertex cut of size whose removal …
5.7 Connectivity - Whitman College
A graph that is not connected consists of connected components. In a theorem reminiscent of this, we see that connected graphs that are not 2-connected are constructed from 2-connected …
Connectivity In Graph Theory - Definition and Examples - BYJU'S
In Mathematics, the meaning of connectivity is one of the fundamental concepts of graph theory. It demands a minimum number of elements (nodes or edges) that require to be removed to …
all the connections in a graph. If the graph is simple, then A is symmetric and has only (a) (b) (c) (d) Figure 1.3: Construction of a line graph. These figures show a graph (a, with blue …
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