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...

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...

We investigate two modifications of the well-known irregularity strength of graphs, namely, a total edge irregularity strength and a total vertex irregularity strength. Recently the bounds and precise values for some families of graphs concerning these parameters have been determined. In this paper, we determine the exact value of the total edge (vertex) irregularity strength for the disjoint u...

Consider a simple graph $G$. We call labeling $w:E(G)\cup V(G)\rightarrow \{1, 2, \dots, s\}$ (\textit{total vertex}) \textit{product-irregular}, if all product degrees $pd_G(v)$ induced by this are distinct, where $pd_G(v)=w(v)\times\prod_{e\ni v}w(e)$. The strength of $w$ is $s$, the maximum number used to label members $E(G)\cup V(G)$. minimum value $s$ that allows some irregular called \tex...

A vertex-irregular total k-labelling λ : V (G)∪E(G) −→ {1, 2, ..., k} of a graph G is a labelling of vertices and edges of G in such a way that for any different vertices x and y, their weights wt(x) and wt(y) are distinct. The weight wt(x) of a vertex x is the sum of the label of x and the labels of all edges incident with x. The minimum k for which a graph G has a vertex-irregular total k-lab...

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.

It is not possible to determine the total vertex of irregular strength all graphs. This study aims ascertain irregularity in prismatic graph amalgamation for n>=4. Determination done by ascertaining largest lower limit and smallest upper limit. The analyzed based on properties other supporting theorems, while labeling vertices edges graph. Based results this study, obtained, namely (4(P2,n))...

Let ( , ) G V E be a simple graph. For a total labeling { } : 1,2,3,..., V E k ∂ ∪ → the weight of a vertex x is defined as ( ) ( ) ( ). xy E wt x x xy ∈ = ∂ + ∂ ∑ ∂ is called a vertex irregular total k-labeling if for every pair of distinct vertices x and y, ( ) ( ). wt x wt y ≠ . The minimum k for which the graph G has a vertex irregular total k-labeling is called the total vertex irregularit...