Problem$-1$: Homogenous amalgamated Star : $S_{n,3}$

$(5$ Marks$)$

For $n3,$ homogenous amalgamated star $S_{n,3}$ admits the edge irregular klabeling.

Order of $S_{n,3}=3n+1.$

Vertex label is at most $k$ and the edge weights are distinctive, thus $S_{n,3}$ admits the edge irregular $k-$labeling.

$k=|$~$\frac{3n+1}{2}$~$|$ Devise an algorithm to assign the labels to the vertices using vertex k$-$

labeling definition