Total edge irregularity strength of disjoint union of double wheel graphs

Total vertex irregularity strength of disjoint union of Helm graphs

A total vertex irregular k-labeling φ of a graph G is a labeling of the vertices and edges of G with labels from the set {1, 2, . . . , k} in such a way that for any two different vertices x and y their weights wt(x) and wt(y) are distinct. Here, the weight of a vertex x in G is the sum of the label of x and the labels of all edges incident with the vertex x. The minimum k for which the graph G...

Total edge irregularity strength of the disjoint union of sun graphs

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...

On Total Edge Irregularity Strength of Staircase Graphs and Related Graphs

Let G=(V(G),E(G)) be a connected simple undirected graph with non empty vertex set V(G) and edge set E(G). For a positive integer k, by an edge irregular total k-labeling we mean a function f : V(G)UE(G) --> {1,2,...,k} such that for each two edges ab and cd, it follows that f(a)+f(ab)+f(b) is different from f(c)+f(cd)+f(d), i.e. every two edges have distinct weights. The minimum k for which G ...

On the Total Irregularity Strength of Disjoint Union of Arbitrary Graphs

Total vertex irregularity strength of wheel related graphs

For a simple graph G with vertex set V (G) and edge set E(G), a labeling φ : V (G) ∪ E(G) −→ {1, 2, . . . , k} is called a vertex irregular total klabeling of G if for any two different vertices x and y, their weights wt(x) ∗ The work was supported by the Higher Education Commission Pakistan. 148 A. AHMAD, K.M. AWAN, I. JAVAID AND SLAMIN and wt(y) are distinct. The weight wt(x) of a vertex x in...