The lower bound of the r -dynamic chromatic number of corona product by wheel graphs

Arika Indah Kristiana, M. Imam Utoyo, Dafik

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

16 Citations (Scopus)

Abstract

The dynamic coloring of a graph G is proper coloring such that every vertex of G with degree has at least two neighbors that are colored differently. A generalization of the dynamic coloring was also introduced by Montgomery in [12], the generalized concept is called r-dynamic k-coloring. An r-dynamic coloring of a graph G is a proper coloring c of the vertices such that |c(N(v)| ≥ min{r, d(v)}, for each v ϵV(G). The r-dynamic chromatic number of a graph G, denoted χr(G) is the smallest k such that c is an r-dynamic k coloring of G. We will find the lower bound of the r-dynamic chromatic number of graphs corona wheel graph and some new results the exact value of r-dynamic chromatic number of corona graphs. In this paper, we study the lower bound of Xr(HWm), Xr(WnH) and we also prove the exact value of r-dynamic chromatic number of some graphs.

Original languageEnglish
Title of host publicationInternational Conference on Science and Applied Science, ICSAS 2018
EditorsM.A. Suparmi, Dewanta Arya Nugraha
PublisherAmerican Institute of Physics Inc.
ISBN (Print)9780735417304
DOIs
Publication statusPublished - 21 Sept 2018
EventInternational Conference on Science and Applied Science, ICSAS 2018 - Surakarta, Indonesia
Duration: 12 May 2018 → …

Publication series

NameAIP Conference Proceedings
Volume2014
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

ConferenceInternational Conference on Science and Applied Science, ICSAS 2018
Country/TerritoryIndonesia
CitySurakarta
Period12/05/18 → …

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