On total H-irregularity strength of the disjoint union of 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...

On the Total Irregularity Strength of Disjoint Union of Arbitrary Graphs

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...

Total vertex irregularity strength of corona product of some graphs

A vertex irregular total k-labeling of a graph G with vertex set V and edge set E is an assignment of positive integer labels {1, 2, ..., k} to both vertices and edges so that the weights calculated at vertices are distinct. The total vertex irregularity strength of G, denoted by tvs(G)is the minimum value of the largest label k over all such irregular assignment. In this paper, we study the to...

On total vertex irregularity strength of graphs

Martin Bača et al. [2] introduced the problem of determining the total vertex irregularity strengths of graphs. In this paper we discuss how the addition of new edge affect the total vertex irregularity strength.