An α -cut chromatic number of a total uncertain graph and its properties

Isnaini Rosyida, Widodo, Ch Rini Indrati, Kiki Ariyanti

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

Abstract

A graph is called an edge uncertain graph if the edges are not deterministic but exist with some belief degrees described by uncertain measure. A new definition for total uncertain graph is first introduced in this paper, that is an uncertain graph in which the vertices and the edges are not deterministic. Further, we give a concept of an α-cut of a total uncertain graph and investigate some of its properties. We color a total uncertain graph via the α-cut, and obtain α-cut chromatic numbers for all α ∈ [0, 1]. Some properties of the α-cut chromatic number are also verified.

Original languageEnglish
Title of host publicationProceedings of the 7th SEAMS UGM International Conference on Mathematics and Its Applications 2015
Subtitle of host publicationEnhancing the Role of Mathematics in Interdisciplinary Research
EditorsYeni Susanti, Indah Emilia Wijayanti, Fajar Adi Kusumo, Irwan Endrayanto Aluicius
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735413542
DOIs
Publication statusPublished - 11 Feb 2016
Event7th SEAMS UGM International Conference on Mathematics and Its Applications: Enhancing the Role of Mathematics in Interdisciplinary Research - Yogyakarta, Indonesia
Duration: 18 Aug 201521 Aug 2015

Publication series

NameAIP Conference Proceedings
Volume1707
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference7th SEAMS UGM International Conference on Mathematics and Its Applications: Enhancing the Role of Mathematics in Interdisciplinary Research
CountryIndonesia
CityYogyakarta
Period18/08/1521/08/15

Keywords

  • Edge uncertain graph
  • total uncertain graph
  • α-cut
  • α-cut chromatic number

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