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Siti Komsatun
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PELABELAN TOTAL TAK REGULER PADA GRAF BARBEL Nugroho Arif Sudibyo; Siti Komsatun
Journal of Mathematics and Mathematics Education Vol 8, No 1 (2018): Journal of Mathematics and Mathematics Education (JMME)
Publisher : Universitas Sebelas Maret

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20961/jmme.v8i1.25818

Abstract

Abstract:For example G (V, E) is a simple graph, a graph that do not contain of loops and parallel sides. Labeling of a graph is a mapping (function) that carries elements of a graph into positive or non-negative integers. Labeling power of irregular total point of a graph is a mapping f: VÈE ® {1, 2, 3, ..., k}which is called as labeling k total irregular point (vertex irregular total k-labeling) in G, if the weight of each different point at G is not the same, that is f(x) + ¹ f(u) + for each of the two points x and u that are different in G.Determination of exact value of irregular power of the total point is done by showing the value of lower limit and upper limit, both of them are proved to have equal value. The upper limit is decided by constructing a label, so that the largest label is obtained by minimum way. According to these two steps, a value for irregular power of the total point of a graph is obtained. In this paper, we will investigate irregular total labeling on barbell graph.Keywords:Point Irregular Total Labeling, Barbell.
PELABELAN TOTAL TAK REGULER PADA BEBERAPA GRAF Nugroho Arif Sudibyo; Siti Komsatun
Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 10 No 2 (2018): Jurnal Ilmiah Matematika dan Pendidikan Matematika
Publisher : Jurusan Matematika FMIPA Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2018.10.2.2840

Abstract

For a simple graph G with vertex set V (G) and edge set E(G), a labeling $\Phi:V(G)\cup U(G)\rightarrow\{1,2,...k\}$ is called a vertex irregular total k- labeling of G if for any two diferent vertices x and y, their weights wt(x) and wt(y) are distinct. The weight wt(x) of a vertex x in G is the sum of its label and the labels of all edges incident with the given vertex x. The total vertex irregularity strength of G, tvs(G), is the smallest positive integer k for which G has a vertex irregular total k-labeling. In this paper, we study the total vertex irregularity strength of some class of graph.
PELABELAN TOTAL TAK REGULER PADA BEBERAPA GRAF Nugroho Arif Sudibyo; Siti Komsatun
Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP) Vol 10 No 2 (2018): Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)
Publisher : Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2018.10.2.2840

Abstract

For a simple graph G with vertex set V (G) and edge set E(G), a labeling $\Phi:V(G)\cup U(G)\rightarrow\{1,2,...k\}$ is called a vertex irregular total k- labeling of G if for any two diferent vertices x and y, their weights wt(x) and wt(y) are distinct. The weight wt(x) of a vertex x in G is the sum of its label and the labels of all edges incident with the given vertex x. The total vertex irregularity strength of G, tvs(G), is the smallest positive integer k for which G has a vertex irregular total k-labeling. In this paper, we study the total vertex irregularity strength of some class of graph.
Co-Authors Nugroho Arif Sudibyo