Rainbow cycles and paths in fan and wheel graph

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Abstract

In this paper we consider optimal edge colored fan graph and wheel graph. On those graph we could obtain rainbow path or cycle, that is path or cycle whose all edges have different colors. We show that there is optimal edge coloring rules for fan graph and wheel graph such that with these coloring we can obtain rainbow cycles with length 3, 4, ⋯, n, with n denotes edge chromatic number and rainbow paths with length 1, 2, ⋯, n.

Original languageEnglish
Title of host publicationProceedings of the 3rd International Symposium on Current Progress in Mathematics and Sciences 2017, ISCPMS 2017
EditorsRatna Yuniati, Terry Mart, Ivandini T. Anggraningrum, Djoko Triyono, Kiki A. Sugeng
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735417410
DOIs
Publication statusPublished - 22 Oct 2018
Event3rd International Symposium on Current Progress in Mathematics and Sciences 2017, ISCPMS 2017 - Bali, Indonesia
Duration: 26 Jul 201727 Jul 2017

Publication series

NameAIP Conference Proceedings
Volume2023
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference3rd International Symposium on Current Progress in Mathematics and Sciences 2017, ISCPMS 2017
CountryIndonesia
CityBali
Period26/07/1727/07/17

Keywords

  • fan graph
  • optimal edge coloring
  • rainbow cycles
  • rainbow paths
  • wheel graph

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