Process

$($a$)$ Convert the graph into a linear system $Ax=0$ where each node is an equation for which the sum of the input equals the sum of the output. For example, node $A$ is represented as $x_1+x_5=0.$

$($b$)$ The minimum spanning tree will be the free variables of the system, found by calculating the reduced row echelon form of the linear system.

$($c$)$ Draw the resulting tree with the redundant edges removed.In graph theory, a spanning tree is a subgraph of some graph $G$ with the minimaw

possible number of edges. In other work, it is an undirected graph in whit there

are no redundant redgo's betwern noder,

The graph in Figure $1$ represents a flow network in which flow ran enter the petwork

at nodes $A,B,C,$ or $D.$ The flow exits the network at node $E.$ Even though the

the graph is a directed graph, the flow can go in either direction of an edge. Find

the spanning tree of the graph.

Process

$($a$)$ Convert the graph iato a linear system. Ax $=0$ where earh node is an equation

for which the sum of the input equals the sum of the output. For example,

aode $A$ is represented as $x_1+x_5=0$

$($b$)$ The: minimam spanning tree will be the free variahles of the system, found by

calculating tbe rodured ruw exblon form of the lincar system,

$($c$)$ Draw the resulting tree with the redundant edges removed.