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...

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...

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...

For a simple graph G, a vertex labeling φ : V (G) → {1, 2, · · · , k} is called k-labeling. The weight of an edge xy in G, denoted by wπ(xy), is the sum of the labels of end vertices x and y, i.e. wφ(xy) = φ(x) + φ(y). A vertex k-labeling is defined to be an edge irregular k-labeling of the graph G if for every two different edges e and f , there is wφ(e) 6= wφ(f). The minimum k for which the g...

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...

For a simple graph G = (V,E) with the vertex set V and the edge set E , a vertex irregular total k -labeling f : V ∪E → {1, 2, . . . , k} is a labeling ∗ Also at Department of Mathematics, Faculty of Mathematics and Sciences, University of Gadjah Mada, Yogyakarta, Indonesia. D. INDRIATI ET AL. /AUSTRALAS. J. COMBIN. 65 (1) (2016), 14–26 15 of vertices and edges of G in such a way that for any t...