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

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 strengt

NILAI KETAKTERATURAN TOTAL SISI DARI GRAF TANGGA PERMATA

Abstract. Let graph G = (V,E) has V vertices and E edges. For every two different edges of graph G has total irregularity strength labelling ofG ifωt(e) ≠ ωt(f) where graph G = (V,E) has V vertices and E edges. The weight edge ofxy of a graph G is (xy) =x) +xy) + y) where x) is the label vertex x and y) is the label vertex y and xy) is the label edge of the xy. The minimum value on the biggest labels make a graph G, has irregular labeling which is defined as total edge irregularity strength and denoted by tes(G). In this article, The total edge irregularity strength of diamond ladder graph and the union of diamond ladder graphs (isomorphic) are determined. The diamond ladder graph, denoted by Dln, is a graph consisting ofn diamond (n ≥2) . Key Words : Total edge irregularity strength, Diamond Ladder Graph (Dln

NILAI KETAKTERATURAN TOTAL SISI DARI GRAF TUNAS KELAPA

Abstract. A total edge irregular labeling on a graph G which has |E| edges and |V| vertices is an assignment of positive integer number as labels to both vertices and edges so that the weights calculated at every edges are distinct. The weight of an edge xy in G is defined as the sum of the label of xy and the labels of two vertices x and y, that is w(xy) = (x)+ (xy)+ (y). The total edge irregularity strength of G, denoted by tes(G), is the smallest positive integer k for which G has an edge-irregular total k-labelling. In this paper, we determine the exact value of the total edge (vertex) irregularity strength of Coconut Sprout Graph (CRn,m) and the union of isomorphic and non-isomorphic Coconut Sprout Graph. Key Words : total edge irregular labeling, total edge irregularity strength, coconut sprout graph

On irregular total labellings

Two new graph characteristics, the total vertex irregularity strength and the total edge irregularity strength, are introduced. Estimations on these parameters are obtained. For some families of graphs the precise values of these parameters are proved. (c) 2006 Elsevier B.V. All rights reserved.C

TOTAL IRREGULARITY STRENGTH OF THREE COPY STAR GRAPH

TOTAL IRREGULARITY STRENGTH OF THREE COPY STAR GRAPH YULIANA NIM:1554201778 Date of Final Exam: 28 July 2020 Date of Graduation: Mathematics Department Faculty of Science and Technology State Islamic University of Sultan Syarif Kasim Riau Jl. HR. Soebrantas No.155 Pekanbaru Abstract Suppose G(V,E) is a graph and k is positive integer. A total k-labeling on a graph G is a mapping that carries of graph elements, denoted by :V∪E→{1,2,…,k} . The weight of the vertex is represented by the sum of every the label of vertex and labels of edges that incident with vertex where as the weight of the edge is represented by the sum of every the label of vertex and label of edges that incident with edge. A total k-labeling λ:V∪E→{1,2,…,k} said irregular total labeling of G, if the weight of the vertex is different and the weight of the edges is also different. The minimum k such that a graph has a totally irregular total k -labeling is called the total irregularity strength of, denoted by ts(G). In this research discusses about the total irregularity strength of three copy star graph, where the set of vertices of each multiplication result is missing. The result of this research, we determine the total irregularity strength of the three copies of star denoted by ts(〖3S〗_n) obtained ts(〖3S〗_n )= Keywords:Tthree copies of star, total irregularity strength, totally irregular total labeling

TOTAL EDGE AND VERTEX IRREGULAR STRENGTH OF TWITTER NETWORK

Twitter data can be converted into a graph where users can represent the vertices. Then the edges can be represented as relationships between users. This research focused on determining the total edge irregularity strength (tes) and the total vertices irregularity strength (tvs) of the Twitter network. The value could be determined by finding the greatest lower bound and the smallest upper bound. The lower bound was determined by using the properties, characteristics of the Twitter network graph along with the supporting theorems from previous studies, while the upper bound is determined through the construction of the total irregular labeling function on the Twitter network. The results in this study are the tes(TW)=18 and tvs(TW)=16

Nilai Total Ketidakteraturan-H pada Graf Cn x P3

AbstrakPenentuan nilai total ketidakteraturan dari semua graf belum dapat dilakukan secara lengkap. Penelitian ini bertujuan untuk menentukan nilai total ketidakteraturan-H pada graf Cn x P3 untuk n ≥ 3 yang isomorfik dengan . Penentuan nilai total ketidakteraturan-H pada graf Cn x P3 dengan menentukan batas bawah terbesar dan batas atas terkecil. Batas bawah dianalisis berdasarkan sifat-sifat graf dan teorema pendukung lainnya. Sedangkan batas atas dianalisa dengan pemberian label pada titik dan sisi pada graf Cn x P3.Berdasarkan hasil penelitian ini diperoleh nilai total ketidakteraturan-H pada graf ths(Cn x P3, C4)=.Kata kunci : Selimut-H, Nilai total ketidakteraturan-HAbstractThe determine of H-irregularity total strength in all graphs was not complete on graph classes. The research aims to determine alghorithm the H-irregularity total strength of graph Cn x P3 for n ≥ 3 with use H-covering, where H is isomorphic to C4. The determine of H-irregularity total strength of graph Cn x P3 was conducted by determining lower bound and smallest upper bound. The lower bound was analyzed based on graph characteristics and other supporting theorem, while the upper bound was analyzed by edge labeling and vertex labeling of graph Cn x P3.The result show that  the H-irregularity total strength of graph ths(Cn x P3, C4)=.Keyword : H-covering, H-irregularity total strengt

Vertex-irregular Labeling and Vertex-irregular Total Labeling on Caterpillar Graph

For a simple graph G with the vertex set V and the edge set E, a labeling ?? : E(G) ?????? {1, 2, ?? ?? ?? , k} is called a vertex-irregular k-labeling on G if for any two different vertices x\ud and y in V we have wt(x) ??= wt(y) where wt(x) =\ud ???\ud z???V ??(xz). The irregularity strength\ud of G, denoted by s(G), is the smallest positive integer k for which G has a vertex-irregular\ud k???labelling. A labeling ?? : V (G) ??? E(G) ?????? {1, 2, ?? ?? ?? , k} is called a vertex-irregular total\ud k-labeling of G if for any two different vertices x and y in V we have wt(x) =?? wt(y) where\ud ???\ud z???V ??(xz). The total vertex irregularity strength of G, denoted by tvs(G), is the smallest positive integer k for which G has a vertex-irregular total k???labelling. In this paper, we determined the irregularity strength and the total vertex irregularity strength of a caterpillar graph

Nilai Ketakteraturan Total dari Lima Copy Graf Bintang

Misalkan G=(V,E) adalah suatu graf dan k adalah suatu bilangan bulat positif. Pelabelan-k total pada G adalah suatu pemetaaan f: V U E?{1,2,...,k}. Bobot titik t dinyatakan dengan wf(t)=f(t)+?ut element E(G)f(ut) dan bobot sisi ut dinyatakan dengan wf(t)=f(u)+f(ut)+f(t). Suatu  pelabelan-k  total  pada G dikatakan tak teratur total, jika bobot setiap titik berbeda dan bobot setiap sisi berbeda. Nilai k terkecil sehingga suatu graf G memiliki pelabelan-k  total tak teratur total disebut nilai ketakteraturan total dari G, dinotasikan dengan ts(G). Pada penelitian ini, ditentukan nilai ketakteraturan total dari lima copy graf bintang 5Sn, dengan n adalah bilangan bulat positif dan n?3. [Let G=(V,E) be a graph and k is a positive integer, total k-labelling on G is a mapping f: V U E?{1,2,...,k}. The weight of the vertex t is defined by wf(t)=f(t)+?ut element E(G)f(ut) and the weight of the edge ut is defined by wf(t)=f(u)+f(ut)+f(t). A total k-labeling of G is called a totally irregular total labeling, if the weight of every two distinct vertices are different and the weight of every two distinct edges are different. The minimum k such that a graph G has a totally irregular total k-labeling of G is called the total irregularity strength of G, denoted by ts(G). In this research determined total irregularity strength of five copies of star graph 5Sn, where n is a positive integer and n?3