TY - JOUR

T1 - The Construction of Labeling and Total Irregularity Strength of Specified Caterpillar Graph

AU - Indriati, Diari

AU - Widodo,

AU - Rosyida, Isnaini

AU - Ariyanti, Kiki

N1 - Publisher Copyright:
© Published under licence by IOP Publishing Ltd.

PY - 2017/6/12

Y1 - 2017/6/12

N2 - Let G be a simple, connected and undirected graph with vertex set V and edge set E. A total k-labeling f : V ∪ E → {1, 2, ⋯, k} is defined as totally irregular total k-labeling if the weights of any two different both vertices and edges are distinct. The weight of vertex x is defined as wt(x) = f(x) + ∑xy∈E f(xy), while the weight of edge xy is wt(xy) = f(x) + f(xy) + f(y). A minimum k for which G has totally irregular total k-labeling is mentioned as total irregularity strength of G and denoted by ts(G). This paper contains investigation of totally irregular total k-labeling for caterpillar graphs Sn,2,m and determination of their total irregularity strengths. In addition, the total vertex and total edge irregularity strength of this graph also be determined. The results are tvs(Sn;2;m) = ⌈n+m-1/2⌉, tes(Sn;2;m) =⌈n+m+2/3⌉ and ts(Sn;2;m) = ⌈n+m-1/2⌉for n, m ≥ 3.

AB - Let G be a simple, connected and undirected graph with vertex set V and edge set E. A total k-labeling f : V ∪ E → {1, 2, ⋯, k} is defined as totally irregular total k-labeling if the weights of any two different both vertices and edges are distinct. The weight of vertex x is defined as wt(x) = f(x) + ∑xy∈E f(xy), while the weight of edge xy is wt(xy) = f(x) + f(xy) + f(y). A minimum k for which G has totally irregular total k-labeling is mentioned as total irregularity strength of G and denoted by ts(G). This paper contains investigation of totally irregular total k-labeling for caterpillar graphs Sn,2,m and determination of their total irregularity strengths. In addition, the total vertex and total edge irregularity strength of this graph also be determined. The results are tvs(Sn;2;m) = ⌈n+m-1/2⌉, tes(Sn;2;m) =⌈n+m+2/3⌉ and ts(Sn;2;m) = ⌈n+m-1/2⌉for n, m ≥ 3.

UR - http://www.scopus.com/inward/record.url?scp=85023630196&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/855/1/012018

DO - 10.1088/1742-6596/855/1/012018

M3 - Conference article

AN - SCOPUS:85023630196

VL - 855

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012018

T2 - 1st International Conference on Mathematics: Education, Theory, and Application, ICMETA 2016

Y2 - 6 December 2016 through 7 December 2016

ER -