On odd harmonious labeling of m -shadow of cycle, gear with pendant and Shuriken graphs

Kiki A. Sugeng, S. Surip, R. Rismayati

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Citation (Scopus)

Abstract

A graph G = (V(G), E(G)) with p vertices and q edges is called (p, q)-graph. An injection f is said to be odd harmonious labeling of a (p, q)-graph G if there is an injective function f from a set of vertices V(G) to a set {0, 1, 2, .., 2q - 1} such that the induced function f from a set of edges E(G) to a set of odd number {1, 3, 5, . 2q - 1} defined by f (uv)=f (u)+f (v) is a bijection. A graph G is said to be odd harmonious if there exists an odd harmonious labeling for G. In this paper we proved that several product graphs, such as m-shadow of cycle Dm (Cn), gear with pendant graphs and Shuriken graphs, are odd harmonious graphs.

Original languageEnglish
Title of host publicationProceedings of the 8th SEAMS-UGM International Conference on Mathematics and Its Applications 2019
Subtitle of host publicationDeepening Mathematical Concepts for Wider Application through Multidisciplinary Research and Industries Collaborations
EditorsHerni Utami, Fajar Adi Kusumo, Nanang Susyanto, Yeni Susanti
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735419438
DOIs
Publication statusPublished - 19 Dec 2019
Event8th SEAMS-UGM International Conference on Mathematics and Its Applications 2019: Deepening Mathematical Concepts for Wider Application through Multidisciplinary Research and Industries Collaborations - Yogyakarta, Indonesia
Duration: 29 Jul 20191 Aug 2019

Publication series

NameAIP Conference Proceedings
Volume2192
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference8th SEAMS-UGM International Conference on Mathematics and Its Applications 2019: Deepening Mathematical Concepts for Wider Application through Multidisciplinary Research and Industries Collaborations
CountryIndonesia
CityYogyakarta
Period29/07/191/08/19

Keywords

  • cycle graph
  • gear graph
  • gear with pendant graph
  • m-shadow graph
  • odd harmonious labeling
  • shuriken graph

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