On super edge-magic total labeling of certain classes of graphs?

A $(p, q)$- simple graph is edge-magic if there exists a bijective function $lambda:V(G)cup E(G)rightarrow {1, 2, dots, p+q}$ such that $lambda(u)+lambda(uv)+lambda(v)=k$, for all edge $uvin E(G),$ where $k$ is called the magic constant or sometimes the valence of $lambda$. An edge-magic total labeling $lambda$ is called super edge-magic total if $lambda(V(G))={1, 2, dots, p}$. In this paper, we construct new classes of trees using w- trees and generalized combs and prove that they admit super edge magic total labeling. We also prove that the extended umbrella graphs admit super edge-magic total labeling.