Inclusive vertex irregular 1-distance labelings on triangular ladder graphs

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

For a simple and connected graph G, the distance between two vertices u, v ϵ V (G), denoted by d(u, v), is the length of the shortest path connecting them. A vertex labeling λ: V (G) → {1, ⋯, k} is called an inclusive vertex irregular d-distance labeling if the weights of the vertices are distinct, where the weight of a vertex v is defined as the sum of the vertex label v and all vertex labels u such that d(u, v) ≤ d. The minimal value of the largest label k of all such labeling of G is called the inclusive d-distance irregularity strength of G and is denoted by disd0(G). Lower and upper bounds for disd0(G) have already been investigated for any graph G with d = 1. The value of dis10(G) for some classes of graphs, such as paths, cycles, complete graphs, and other related types of graphs, have also been determined in the literature. In this paper, we find an upper bound for dis10(G) for triangular ladder graphs Ln, with n ≡ 4 mod 5, n > 4, and the exact value for the rest of the cases with n ≥ 3.

Original languageEnglish
Title of host publication8th Annual Basic Science International Conference
Subtitle of host publicationCoverage of Basic Sciences toward the World's Sustainability Challenges
EditorsCorina Karim, Rodliyati Azrianingsih, Mauludi Ariesto Pamungkas, Yoga Dwi Jatmiko, Anna Safitri
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735417397
DOIs
Publication statusPublished - 17 Oct 2018
Event8th Annual Basic Science International Conference: Coverage of Basic Sciences toward the World's Sustainability Challanges, BaSIC 2018 - Malang, East Java, Indonesia
Duration: 6 Mar 20187 Mar 2018

Publication series

NameAIP Conference Proceedings
Volume2021
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference8th Annual Basic Science International Conference: Coverage of Basic Sciences toward the World's Sustainability Challanges, BaSIC 2018
CountryIndonesia
CityMalang, East Java
Period6/03/187/03/18

Keywords

  • inclusive d-distance irregularity strength
  • triangular ladder graph
  • vertex labelling

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  • Cite this

    Utami, B., Ariyanti, K., & Utama, S. (2018). Inclusive vertex irregular 1-distance labelings on triangular ladder graphs. In C. Karim, R. Azrianingsih, M. A. Pamungkas, Y. D. Jatmiko, & A. Safitri (Eds.), 8th Annual Basic Science International Conference: Coverage of Basic Sciences toward the World's Sustainability Challenges [060006] (AIP Conference Proceedings; Vol. 2021). American Institute of Physics Inc.. https://doi.org/10.1063/1.5062770