Edge Covers and Edge Covering Numbers of Graphs | Graph Theory

We introduce edge covers, edge covering numbers, and minimum edge covers of graphs. An edge cover of a graph G is a set L such that every vertex of G is incident to some edge of L. Every graph with no isolated vertices has an edge cover. An edge cover of minimum cardinality is a minimum edge cover, and the cardinality of such a cover is the edge covering number of the graph. We see some edge cover examples and discuss some facts about edge covers of graphs. #graphtheory
Vertex Covers and Vertex Covering Numbers: • Vertex Covers and Vert...
Graph Theory course: • Graph Theory
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[@WrathofMath]

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[@riyarocks]

Thank you❤

[@WrathofMath]

You're welcome !

[@MalithClicks]

Thank you so much ! ❤🎉

[@WrathofMath]

My pleasure! There is much more to say on this topic, and more videos will come in the future!

[@MalithClicks]

​@@WrathofMath thats great ! 😮🎉

[@user-wr4yl7tx3w]

Is there a way to see the motivation of why this could be useful?

[@rabomeister]

I mean I'm not sure but you can lower it a bit by selecting a root edge or vertex as a base point then you can use edge cover to find least expensive communication paths, for example in software development. Also, in cryptography research -especially in coins nowadays- you need to validate your transaction to nodes, which are vertices. I guess they might be proper candidates.

[@PunmasterSTP]

Ah, another edgy video...