Let G be an undirected connected graph whose edge weights are positive

and distinct. We know that the MST is unique when the edge weights

are distinct. Now, consider the set of all the spanning trees without the

MST$.$ The spanning tree with the minimum weight in this set is defined as asecond$-$bestminimumspanningtree$($SBMST$).$Bywayofanexample,Mean$1\mathrm{.}9$

illustrate that a SBMST need not be unique.

In order to get complete credit, you need to show

$($a$)$ a graph that satisfies the conditions of the question $($b$)$ MST of this graph

$($c$)$ at least two SBMST for this graph

$[4$ marks$]$

$[1$ mark$]$

$[1$ mark$][2$ marks$]$