Irregular labelings of helm and sun graphs

A vertex irregular total kk-labeling of a (p,q)(p,q)-graph G=(V,E)G=(V,E) is a labeling ϕ:V∪E→{1,2,…,k}ϕ:V∪E→{1,2,…,k} such that the weights of the vertices wt(v)=ϕ(v)+∑uv∈Eϕ(uv)wt(v)=ϕ(v)+∑uv∈Eϕ(uv) are different for all vertices. The total vertex irregularity strength tvs(G)tvs(G) is the minimum kk for which GG has a vertex irregular total kk-labeling. The labeling ϕϕ is an edge irregular total kk-labeling if for any two distinct edges e1=u1v1e1=u1v1 and e2=u2v2e2=u2v2, one has wt(e1)≠wt(e2)wt(e1)≠wt(e2) where wt(e1)=ϕ(u1)+ϕ(v1)+ϕ(u1v1)wt(e1)=ϕ(u1)+ϕ(v1)+ϕ(u1v1). The total edge irregularity strength tes(G)tes(G) is the minimum kk for which GG has an edge irregular total kk-labeling. In this paper we determine tes(G)tes(G) where GG is the generalized helm and tvs(G)tvs(G) where GG is the generalized sun graph.