You are given the following adjacency$-$matrix representation of a weighted undirected graph.

i$.$ Draw the resulting minimum spanning tree output of the Kruskal's algorithm given in the

A$!$

ii$.$ What is$/$are the light edge$($s$)$ of the graph defined by the cut $(\{A,B\},\{C,D,E\})?$

$(A,D)$

iii. Does the cut defined in part $($ii$)$ respects to set $\{B,D,E\}?$ Why $?$ Why not?

No$.$ Because, the cut causes node $B$

node $D$ to be in differeut portitions, as an exaple.

iv$.$ In general, let $e$ be a minimum$-$weight edge of a connected weighted graph. Can you say

that "Edge e must be one of the edges of each minimum spanning tree of the graph". Explain

your answer by giving an example.

No$.$ Consider below graph having the same edge

$ow$ graph having the same eage

$cost.(A,B)is$ one $of$ the mimimut

height edges howerer $itis$ not

one $of$ the edqes $of$ possibb cminun

spanning tree defined $as$: $A$

neight edges however it is not