Total Edge Irregularity Strength of the Disjoint Union of Sun Graphs
Muhammad Kamran Siddiqui, Ali Hasan Ahmad, Muhammad Faisal Nadeem, Yasir Bashir · International Journal of Mathematics and Soft Computing · 2013
An edge irregular total k-labeling ϕ: V ∪ E → {1, 2,..., k} of a graph G = (V,E) is a labeling of vertices and edges of G in such a way that for any different edges uv and u′v ′ their weights ϕ(u) +ϕ(uv) +ϕ(v) and ϕ(u′) +ϕ(u′v′) +ϕ(v′) are distinct. The total edge irregularity strength, tes(G), is defined as the minimum k for which G has an edge irregular total k-labeling. In this paper, we consider the total edge irregularity strength of the disjoint union of p isomorphic sun graphs, tes(pMn), disjoint union of p consecutive non-isomorphic sun graphs, tes(⋃pj=1Mnj).