Harmonious labeling of the union of m-cycle and n-path graph

S. Ng, F. Alwie, T. P. Marjadi, K. A. Sugeng

Research output: Contribution to journalConference articlepeer-review

Abstract

A graph G is called harmonious graph if there is an injective mapping f from the set of vertices of G to the set Zq so that the mapping induced a bijection mapping f* from the set of edges of G to Zq, which is defined as f *(xy) = f (x) + f (y) for each edge xy∈ E(G). The mapping f is called harmonious labeling. Harmonious labeling concept has been developed since 1980. At that time, harmonious labeling is inspired by channel assignment problems. Nowadays, harmonious labeling has been known for various classes of graphs. However, there are still many certain classes of graphs that have not been determined yet whether they can be harmonious labeled or not. One of the class of graphs that have not been determined yet whether it can be harminous labeled or not is graph Cm ∪ Pn. In this paper, we prove that there is a harmonious labeling of graph Cm ∪ Pn for some values m and.

Original languageEnglish
Article number012088
JournalJournal of Physics: Conference Series
Volume1725
Issue number1
DOIs
Publication statusPublished - 12 Jan 2021
Event2nd Basic and Applied Sciences Interdisciplinary Conference 2018, BASIC 2018 - Depok, Indonesia
Duration: 3 Aug 20184 Aug 2018

Keywords

  • Cycle
  • Harmonious labeling
  • Labeling
  • Path
  • Union of graph

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