Omar is labelling weights on the graph G

shown below. Currently they have labelled the edges AB

and AC

$,$ but the remaining edges do not yet have weights given to them. Omar refers to the weights of BC

$,$ CD

$,$ and BD

as x

$,$ y

$,$ and z

respectively.

Maple plot

$($a$)$ Find positive integer values for x$,$y$,$z

such that both

the edge BC

is not contained in any minimal spanning tree of G

$,$ and

the edge BC

is contained in a shortest path from C

to D