6.4 Minimum Spanning Tree | Properties of MST | Data Structures Tutorials

In this lecture, I have explained Minimum Spanning Tree with its Properties and with example.
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[@nazmussakib1806]

Right

[@tarachandrahul1203]

02:00 Minimum spanning trees are a subset of a given graph that contain the same number of vertices and a number of edges that is equal to the number of vertices minus 1.
04:00 Minimum spanning tree is a tree that contains the same number of vertices as the graph and the number of edges in the spanning tree is one less than the number of vertices in the graph.
06:00 The minimum spanning tree is the spanning tree with the lowest total edge weight.
08:00 Minimum Spanning Tree (MST) is a tree with the minimum edge cost among all the possible spanning trees.
10:00 Properties of Minimum Spanning Tree
12:00 A complete graph of 4 vertices can have maximum 16 spanning trees.
14:00 A complete graph has all pairs of vertices connected by one edge
15:58 Properties of Minimum Spanning Tree

[@yashpandey350]

Small help for English students: Conversion of each Hindi sentence/words in English.Sorry for 1 second + -
0:34: Now spanning tree of this graph would be
3:31: So, Many spanning trees
6:20: Minimum spanning tree is that whose total cost/weight of spanning tree is minimum out of all spanning trees' minimum cost/weight.
7:27: Ok, see
7:38: If you remove a single edge, a single one than that spanning tree would be disconnected
7:55: So as many as edges in the spanning tree
8:13: Distinct means different weights/costs, which means there is no same weight of any edge.
8:21: There will only single MST and that would be unique
8:26: If the edge case is not distinct then
8:31: Suppose we have one graph and which has two or three edges whose weight is same this this this like that ok
8:47: And
9:17: This is the condition when edge weights are
9:33: Talking about a complete graph. Complete graphs are those if each vertex of that graph is connected with another vertex.
9:53: Here n is n to the power n-2, where n is the number of vertices of that graph.
10:35: This will not happen that the graph is connected and it has no spanning tree. And that is not possible at least it has one spanning tree.
10:57: Ok
11:22: Ok
11:32: Maximum edges can be removed are
12:06: So maximum edges you can remove from this graph are
12:10: What are its spanning trees, and spanning trees properties are
12:24: Means how many edges
13:00: So maximum edge you can remove only one
13:04: We removed 1 and we got this spanning tree
13:50: Complete graph has this property
13:55: Now one of Its spanning trees, let us first draw all of its vertices.
14:06: Number of edges would be
14:13: Three edge could be that
14:35: So maximum edges you can remove from this graph is (e-n+1)
14:41: How many numbers of edges
14:58: Ok, and how many edges we removed from this graph are: these three edges we have and we removed these three edges and if you remove another edge then this graph would be disconnected.
15:20: So the maximum you can remove only
15:32: Main properties, I already told you that there would be the same number of vertices and edges would be
15:47: One more property of spanning-tree we can add
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[@samiulislamdurjoy]

G 244
two condition of spaning tree
1. V'=V
2. E'=|V|-1
note: spanning tree should not contain any cycle
note: To find Minimum spanning tree, eliminate maximum costed edge
note: golden basic from7:19-final

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[@paragggoyal1552]

That last property why is it written maximum, shouldn't the term used be 'exactly' in place of 'maximum'?
Also, why only complete graph, won't all connected graphs holds that property true?
e - n + 1 = e-(n-1).
and (n-1) is the number of edges in a spanning tree, therefore, in all connected graphs having 'e' edges, we have to remove 'e-(n-1)'. == 'e-n+1'. Exactly.
Am I wrong??
Please reply.

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