For n $>=3,$ homogenous amalgamated

star Sn$,$m admits the edge irregular k$-$

labeling.

$$ Order of Sn$,$m $=$ m x n $+1$

$$ Vertex label is at most k and the edge

weights are distinctive, thus Sn$,$m admits

the edge irregular k$-$labeling.

k$=$ceil$($m$*$n$+1/2)$

$1.$ Find out the best data$-$structure to represent $/$ store the graph in memory.

$2.$ Devise an algorithm to assign the labels to the vertices using vertex k$-$

labeling definition. $($Main Task$)$

$3.$ What design strategy you will apply, also give justifications that selected

strategy is most appropriate.

$4.$ How traversing will be applied?

$5.$ Store the labels of vertices and weights of the edges as an outcome.

$6.$ Compare your results with mathematical property and tabulate the

outcomes for comparison.

$7.$ Hardware resources supported until what maximum value of n$,$ m$.$

$8.$ Compute the Time Complexity of your algorithm T$($V$,$E$)$ or T$($n$)$

conditions:

Output should be a graph

Edge weights should start from $2$ and They should be in sequence with all the edge weights

edge weights should be calculated such that sum of $2$ vertex labels

Vertex labels can be same or different

if the solution is with centroid vertex $1$ it will be easy

k is already mentioned in the problems

In Output graph, max vertex label value and k value should be same