# KEdgeConnectedGraphQ

KEdgeConnectedGraphQ[g,k]

yields True if the graph g is k-edge-connected and False otherwise.

# Details

• A graph is k-edge-connected if there are at least k edge-disjoint paths between every pair of vertices.

# Examples

open allclose all

## Basic Examples(2)

Test whether a graph is 2-edge-connected:

A graph with isolated vertices is not k-edge-connected:

## Scope(5)

Test undirected graphs:

Directed graphs:

Multigraphs:

Mixed graphs:

KEdgeConnectedGraphQ gives False for anything that is not a k-connected graph:

## Properties & Relations(3)

The complete graph is -edge-connected:

An undirected tree is 1-edge-connected:

A k-edge-connected graph has edge connectivity greater than or equal to k:

Wolfram Research (2014), KEdgeConnectedGraphQ, Wolfram Language function, https://reference.wolfram.com/language/ref/KEdgeConnectedGraphQ.html.

#### Text

Wolfram Research (2014), KEdgeConnectedGraphQ, Wolfram Language function, https://reference.wolfram.com/language/ref/KEdgeConnectedGraphQ.html.

#### CMS

Wolfram Language. 2014. "KEdgeConnectedGraphQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/KEdgeConnectedGraphQ.html.

#### APA

Wolfram Language. (2014). KEdgeConnectedGraphQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/KEdgeConnectedGraphQ.html

#### BibTeX

@misc{reference.wolfram_2024_kedgeconnectedgraphq, author="Wolfram Research", title="{KEdgeConnectedGraphQ}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/KEdgeConnectedGraphQ.html}", note=[Accessed: 15-June-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_kedgeconnectedgraphq, organization={Wolfram Research}, title={KEdgeConnectedGraphQ}, year={2014}, url={https://reference.wolfram.com/language/ref/KEdgeConnectedGraphQ.html}, note=[Accessed: 15-June-2024 ]}