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
SN - 1431-0635
VL - 25
SP - 309
EP - 329
JO - Documenta Mathematica
JF - Documenta Mathematica
IS - 6
ER -