Total Vertex Irregularity Strength Research Articles

ON THE TOTAL VERTEX IRREGULARITY STRENGTH OF SERIES PARALLEL GRAPH sp(m,r,4)

his study aims to determine the total vertex irregularity strength on a series parallel graph for and . Total labeling is said to be vertex irregular, if the weights for each vertices are different. Determination of the total vertex irregularity of series parallel graph is done by obtaining the largest lower bound and the smallest upper bound. The lower bound is obtained by analyzing the structure of the graph to obtain the largest minimum label of k and the upper bound is analyzed by labeling the vertices and edges of the graph, where the largest label is k and the values for each vertices weight is different. The result obtained for the total vertex irregularity strength of a series parallel graph is .

Total Vertex Irregularity Strength Of Prismatic Graph Amalgamation

It is not possible to determine the total vertex of irregular strength of all graphs. This study aims to ascertain the total vertex irregularity strength in prismatic graph amalgamation for n>=4. Determination of the total vertex irregularity strength in prismatic graph amalgamation is done by ascertaining the largest lower limit and the smallest upper limit. The lower limit is analyzed based on the graph properties and other supporting theorems, while the upper limit is analyzed by labeling the vertices and edges of the prismatic amalgamation graph. Based on the results of this study, the total vertex irregularity strength in prismatic graph amalgamation is obtained, namely (4(P2,n))=2n , for n>=4.

Total distance vertex irregularity strength of some corona product graphs

A distance vertex irregular total k -labeling of a simple undirected graph G = G ( V , E ) , is a function f : V ( G )∪ E ( G )→{1, 2, …, k } such that for every pair vertices u , v ∈ V ( G ) and u ≠ v , the weights of u and v are distinct. The weight of vertex v ∈ V ( G ) is defined to be the sum of the label of vertices in neighborhood of v and the label of all incident edges to v . The total distance vertex irregularity strength of G (denoted by t d i s ( G ) ) is the minimum of k for which G has a distance vertex irregular total k -labeling. In this paper, we present several results of the total distance vertex irregularity strength of some corona product graphs.

Modular total vertex irregularity strength of graphs

<abstract><p>A (modular) vertex irregular total labeling of a graph $ G $ of order $ n $ is an assignment of positive integers from $ 1 $ to $ k $ to the vertices and edges of $ G $ with the property that all vertex weights are distinct. The vertex weight of a vertex $ v $ is defined as the sum of numbers assigned to the vertex $ v $ itself and to the edge's incident, while the modular vertex weight is defined as the remainder of the division of the vertex weight by $ n $. The (modular) total vertex irregularity strength of $ G $ is the minimum $ k $ for which such labeling exists. In this paper, we obtain estimations on the modular total vertex irregularity strength, and we evaluate the precise values of this invariant for certain graphs.</p></abstract>

The total vertex irregularity strength of symmetric cubic graphs of the Foster's Census

<p>Foster (1932) performed a mathematical census for all connected symmetric cubic (trivalent) graphs of order <em>n</em> with <em>n </em>≤ 512. This census then was continued by Conder et al. (2006) and they obtained the complete list of all connected symmetric cubic graphs with order <em>n</em> ≤ 768. In this paper, we determine the total vertex irregularity strength of such graphs obtained by Foster. As a result, all the values of the total vertex irregularity strengths of the symmetric cubic graphs of order <em>n</em> from Foster census strengthen the conjecture stated by Nurdin, Baskoro, Gaos & Salman (2010), namely ⌈(<em>n</em>+3)/4⌉.</p>

Two types irregular labelling on dodecahedral modified generalization graph

Irregular labelling on graph is a function from component of graph to non-negative natural number such that the weight of all vertices, or edges are distinct. The component of graph is a set of vertices, a set of edges, or a set of both. In this paper we study two types of irregular labelling on dodecahedral modified generalization graph. We determined the total vertex irregularity strength and the modular irregularity strength of dodecahedral modified generalized graph. These results are important because there many classes of graph have the same structure with modified dodecahedral graphs. These results can be used to determine the total vertex irregularity strength and the modular irregularity strength of other graphs that have the similar structure with modified dodecahedral graph.

PELABELAN TOTAL TIDAK TERATUR TITIK GRAF UNIDENTIFIED FLYING OBJECT

For a graph G that have vertex set V and edge set E. A labelling f:VUE->{1,2,3,...,k} is called a vertex irregularity total k-labeling of G if for any two different vertices x and y in V have wt(x)\neq wt(y) where wt(x)=f(x)+ ∑_{yV(G)} f(xy). The smallest positive integer k such that G has a vertex irregular total k-labeling is called the total vertex irregularity strength of G , denoted by tvs(G) . In this paper, we determined the total vertex irregularity strength of Unidentified Flying Object Graph, tvs(U_(m,n}) . The result in this paper as follows: tvs(U_{m,n})=(3n+1)/2 for 3<=m<=3((n+1)/2), n>=3, and tvs(U_{m,n})=(3n+m)/3 for m>3((n+1)/2), n>=3.

Total Irregularity Strengths of a Disjoint Union of (4,6)-Fullerene Graphs

A fullerene is a polyhedral molecule made entirely of carbon atoms other than graphite and diamond. Mathematical chemistry or Chemical graph theory as a combination of chemistry and graph theory studies the physical properties of mathematically modeled chemical compounds. Graph labeling is a vital area of graph theory that has applications in both physical and social sciences. For example, in chemistry vertex labeling is used in the constitution of valence isomers and transition labeling to study chemical reaction networks. A (4,6)-fullerene graph is a mathematical model of a (4,6)-fullerene molecule. It is a cubic-regular planar graph whose faces are squares and hexagons. In this article, we study the total vertex irregularity strength and the total edge irregularity strength of a disjoint union of (4,6)-fullerene graphs and provide their exact values.

Total Irregularity Strengths of an Arbitrary Disjoint Union of (3,6)- Fullerenes.

A fullerene graph is a mathematical model of a fullerene molecule. A fullerene molecule, or simply a fullerene, is a polyhedral molecule made entirely of carbon atoms other than graphite and diamond. Chemical graph theory is a combination of chemistry and graph theory, where theoretical graph concepts are used to study the physical properties of mathematically modeled chemical compounds. Graph labeling is a vital area of graph theory that has application not only within mathematics but also in computer science, coding theory, medicine, communication networking, chemistry, among other fields. For example, in chemistry, vertex labeling is being used in the constitution of valence isomers and transition labeling to study chemical reaction networks Method: In terms of graphs, vertices represent atoms while edges stand for bonds between the atoms. By tvs (tes) we mean the least positive integer for which a graph has a vertex (edge) irregular total labeling such that no two vertices (edges) have the same weights. A (3,6)-fullerene graph is a non-classical fullerene whose faces are triangles and hexagons Results: Here, we study the total vertex (edge) irregularity strength of an arbitrary disjoint union of (3,6)-fullerene graphs and provide their exact values. The lower bound for tvs (tes) depends on the number of vertices. Minimum and maximum degree of a graph exist in literature, while to get different weights, one can use sufficiently large numbers, but it is of no interest. Here, by proving that the lower bound is the upper bound, we close the case for (3,6)-fullerene graphs.

Computing the Total Vertex Irregularity Strength Associated with Zero Divisor Graph of Commutative Ring

Let R be a commutative ring and Z(R) be the set of all zero divisors of R. Γ(R) is said to be a zero divisor graph if x,y ∈ V (Γ(R)) = Z(R) and (x,y) ∈ E(Γ(R)) if and only if x.y = 0. In this paper, we determine the total vertex irregularity strength of zero divisor graphs associated with the commutative rings ℤp2 × Zq for p,q prime numbers.

Some Types of Irregular Labeling of Diamond Networks on Ten Vertices

There are three interesting parameters in irregular networks based on total labelling, i.e. the total vertex irregularity strength, the total edge irregularity strength, and the total irregularity strength of a graph. Besides that, there is a parameter based on edge labelling, i.e., the irregular labelling. In this paper, we determined the four parameters for diamond graph on eight vertices.

On the total irregularity strength of convex polytope graphs

A vertex (edge) irregular total k-labeling ? 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 any two different vertices (edges) have distinct weights. 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, whereas the weight of an edge is the sum of label of the edge and the vertices incident to that edge. The minimum k for which the graph G has a vertex (edge) irregular total k-labeling is called the total vertex (edge) irregularity strength of G. In this paper, we are dealing with infinite classes of convex polytopes generated by prism graph and antiprism graph. We have determined the exact value of their total vertex irregularity strength and total edge irregularity strength.

On Total Vertex Irregularity Strength of Hexagonal Cluster Graphs

For a simple graph G with a vertex set V G and an edge set E G , a labeling f : V G ∪ ​ E G ⟶ 1,2 , ⋯ , k is called a vertex irregular total k − labeling of G if for any two different vertices x and y in V G we have w t x ≠ w t y where w t x = f x + ∑ u ∈ V G f x u . The smallest positive integer k such that G has a vertex irregular total k − labeling is called the total vertex irregularity strength of G , denoted by tvs G . The lower bound of tvs G for any graph G have been found by Baca et. al. In this paper, we determined the exact value of the total vertex irregularity strength of the hexagonal cluster graph on n cluster for n ≥ 2 . Moreover, we show that the total vertex irregularity strength of the hexagonal cluster graph on n cluster is 3 n 2 + 1 / 2 .

Total vertex irregularity strength of generalized prism graphs

A total k-labeling φ : V ∪ E → {1, 2, 3,…, k} is called a vertex irregular total k-labeling, if wt(a) ≠ wt(b), for x ≠ y ∈V, The weight of a vertex is defined as: , where N(a) is the set of neighbors of a. The minimum value of k for a vertex irregular total k-labeling is called the total vertex irregularity strength of G, tvs(G) [7]. Recently, many authors are studying the two well-known modifications of irregularity strength of graphs, namely, the total edge irregularity strength and the total vertex irregularity strength of graphs. In this paper we study the total vertex irregularity strength of the generalized prism .

Total vertex irregularity strength for trees with many vertices of degree two

For a simple graph G = ( V,E ) , a mapping φ : V ∪ E → { 1 , 2 ,..., k } is defined as a vertex irregular total k -labeling of G if for every two different vertices x and y , wt ( x ) ≠ wt ( y ), where wt ( x ) = φ ( x )+ Σ􏰄 xy ∈ E ( G ) φ ( xy ). The minimum k for which the graph G has a vertex irregular total k -labeling is called the total vertex irregularity strength of G . In this paper, we provide three possible values of total vertex irregularity strength for trees with many vertices of degree two. For each of the possible values, sufficient conditions for trees with corresponding total vertex irregularity strength are presented.

On the Total Vertex Irregular Labeling of Proper Interval Graphs

A labeling of a graph is a mapping that maps some set of graph elements to a set of numbers (usually positive integers). For a simple graph G = (V, E) with vertex set V and edge set E, a labeling Φ: V ∪ E → {1, 2, ..., k} is called total k-labeling. The associated vertex weight of a vertex x∈ V under a total k-labeling Φ is defined as wt(x) = Φ(x) + ∑y∈N(x) Φ(xy) where N(x) is the set of neighbors of the vertex x. A total k-labeling is defined to be a vertex irregular total labeling of a graph, if for every two different vertices x and y of G, wt(x)≠wt(y). The minimum k for which a graph G has a vertex irregular total k-labeling is called the total vertex irregularity strength of G, tvs(G). In this paper, total vertex irregularity strength of interval graphs is studied. In particular, an efficient algorithm is designed to compute tvs of proper interval graphs and bounds of tvs is presented for interval graphs.

Total Irregular Labelling Of Butterfly and Beneš Network 5-Dimension

This paper aims to determine the total vertex irregularity strength and total edge irregularity strength of Butterfly and Beneš Network 5-Dimension. The determination of the total vertex irregularity strength and the edge irregularity strength was conducted by determining the lower bound and upper bound. The lower bound was analyzed based on characteristics of the graph and other proponent theorems, while upper bound was analyzed by constructing the function of the irregular total labeling. The result show that the total vertex irregularity strength of Butterfly Network , the total edge irregularity strength . The total vertex irregularity strength of Beneš Network , the total edge irregularity strength

On total vertex irregularity strength of generalized uniform cactus chain graphs with pendant vertices

In this research, we use the concept of a vertex irregular total k labeling and tvs(G). Specifically, we investigate tvs of generalized uniform cactus chain graphs with (n – 2)r pendant vertices and length r. The result is as follows: for n ≥ 6.

On total edge and total vertex irregularity strength of pentagon cactus chain graph with pendant vertices

Let G(V, E) be a graph with a non-empty set of vertices V and a set of edges E. A total k-labeling f: V ∪ E → {1,2, …, k} is called an edge irregular total k-labeling if the weight of each edge is distinct, where the weight of an edge e = xy is wt(e) = f(xy) + f(x) + f(y). Whereas, f is a vertex irregular total k-labeling if the weight wt(x) ≠ wt(y) for two distinct vertices x, y of V(G) where the weight wt(x) = f(x) + ∑ υx∈E(G) f(υx).The minimum k for which G has an edge irregular total k-labeling is called the total edge irregularity strength (tes) of G. Further, the total vertex irregularity strength (tvs) of G is the minimum k for which G has a vertex irregular total k-labeling. In this paper, we find tes and tvs of heptagon cactus chain graph with pendants and get the results as follows: tes and tvs .

Total Vertex Irregularity Strength of Disjoint Union of Ladder Rung Graph and Disjoint Union of Domino Graph

We investigate a graph labeling called the total vertex irregularity strength (tvs(G)). A tvs(G) is minimum for which graph has a vertex irregular total -labeling. In this paper, we determine the total vertex irregularity strength of disjoint union of ladder rung graph and disjoint union of domino graph.