Find in Library
Search millions of books, articles, and more
Indexed Open Access Databases
Irregular labelings of helm and sun graphs
oleh: Ali Ahmad, Misbah Arshad, Gabriela Ižaríková
Format: | Article |
---|---|
Diterbitkan: | Taylor & Francis Group 2015-11-01 |
Deskripsi
A vertex irregular total k-labeling of a (p,q)-graph G=(V,E) is a labeling ϕ:V∪E→{1,2,…,k} such that the weights of the vertices wt(v)=ϕ(v)+∑uv∈Eϕ(uv) are different for all vertices. The total vertex irregularity strength tvs(G) is the minimum k for which G has a vertex irregular total k-labeling. The labeling ϕ is an edge irregular total k-labeling if for any two distinct edges e1=u1v1 and e2=u2v2, one has wt(e1)≠wt(e2) where wt(e1)=ϕ(u1)+ϕ(v1)+ϕ(u1v1). The total edge irregularity strength tes(G) is the minimum k for which G has an edge irregular total k-labeling. In this paper we determine tes(G) where G is the generalized helm and tvs(G) where G is the generalized sun graph.