TY - GEN

T1 - On total irregularity strength of star graphs, double-stars and caterpillar

AU - Indriati, Diari

AU - Widodo,

AU - Wijayanti, Indah E.

AU - Ariyanti, Kiki

PY - 2016/2/11

Y1 - 2016/2/11

N2 - For a simple graph G = (V, E) with the vertex set V and the edge set E, a totally irregular total k-labeling f: V U E → {1, 2,..., k} is a labeling of vertices and edges of G in such a way that for any two different vertices x and x', their weights wt f(x) = f(x) + Σxy∈E f (xy) and wtf (x') = f (x') + Σx' y' ∈E f (x'y') are distinct, and for any two different edges xy and x'y' their weights f (x) + f (xy) + f (y) and f (x') + f (x'y') + f (y') are also distinct. A total irregularity strength of graph G, denoted by ts(G), is defined as the minimum k for which G has a totally irregular total k-labeling. In this paper, we determine the exact value of the total irregularity strength for star graphs, double stars and caterpillar.

AB - For a simple graph G = (V, E) with the vertex set V and the edge set E, a totally irregular total k-labeling f: V U E → {1, 2,..., k} is a labeling of vertices and edges of G in such a way that for any two different vertices x and x', their weights wt f(x) = f(x) + Σxy∈E f (xy) and wtf (x') = f (x') + Σx' y' ∈E f (x'y') are distinct, and for any two different edges xy and x'y' their weights f (x) + f (xy) + f (y) and f (x') + f (x'y') + f (y') are also distinct. A total irregularity strength of graph G, denoted by ts(G), is defined as the minimum k for which G has a totally irregular total k-labeling. In this paper, we determine the exact value of the total irregularity strength for star graphs, double stars and caterpillar.

KW - caterpillar

KW - double stars

KW - star

KW - total irregularity strength

KW - totally irregular total k-labeling

UR - http://www.scopus.com/inward/record.url?scp=84984539086&partnerID=8YFLogxK

U2 - 10.1063/1.4940809

DO - 10.1063/1.4940809

M3 - Conference contribution

AN - SCOPUS:84984539086

T3 - AIP Conference Proceedings

BT - Proceedings of the 7th SEAMS UGM International Conference on Mathematics and Its Applications 2015

A2 - Susanti, Yeni

A2 - Wijayanti, Indah Emilia

A2 - Kusumo, Fajar Adi

A2 - Aluicius, Irwan Endrayanto

PB - American Institute of Physics Inc.

T2 - 7th SEAMS UGM International Conference on Mathematics and Its Applications: Enhancing the Role of Mathematics in Interdisciplinary Research

Y2 - 18 August 2015 through 21 August 2015

ER -