TY - JOUR

T1 - Totally irregular total labeling of some caterpil-lar graphs

AU - Indriati, Diari

AU - Widodo,

AU - Wijayanti, Indah E.

AU - Sugeng, Kiki A.

AU - Rosyida, Isnaini

N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020

Y1 - 2020

N2 - Assume that G(V, E) is a graph with V and E as its vertex and edge sets, respectively. We have G is simple, connected, and undirected. Given a function λ from a union of V and E into a set of k-integers from 1 until k. We call the function λ as a totally irregular total k-labeling if the set of weights of vertices and edges consists of different numbers. For any u € V, we have a weight ***. Also, it is defined a weight ***. A minimum k used in k-total labeling λ is named as a total irregularity strength of G, symbolized by ts(G). We discuss results on ts of some caterpillar graphs in this paper. The results are *** for p,q greater than or equal to 3, while ****.

AB - Assume that G(V, E) is a graph with V and E as its vertex and edge sets, respectively. We have G is simple, connected, and undirected. Given a function λ from a union of V and E into a set of k-integers from 1 until k. We call the function λ as a totally irregular total k-labeling if the set of weights of vertices and edges consists of different numbers. For any u € V, we have a weight ***. Also, it is defined a weight ***. A minimum k used in k-total labeling λ is named as a total irregularity strength of G, symbolized by ts(G). We discuss results on ts of some caterpillar graphs in this paper. The results are *** for p,q greater than or equal to 3, while ****.

KW - caterpillar graph

KW - total irregularity strength

KW - totally irregular total k-labeling

KW - weight

UR - http://www.scopus.com/inward/record.url?scp=85097416665&partnerID=8YFLogxK

U2 - 10.5614/ejgta.2020.8.2.5

DO - 10.5614/ejgta.2020.8.2.5

M3 - Article

AN - SCOPUS:85097416665

VL - 25

SP - 309

EP - 329

JO - Documenta Mathematica

JF - Documenta Mathematica

SN - 1431-0635

IS - 6

ER -