Tattooing and the Tattoo Number of Graphs

Title

Tattooing and the Tattoo Number of Graphs

Creator

Kok J.; Naduvath S.

Description

Consider a network D of pipes which have to be cleaned using some cleaning agents, called brushes, assigned to some vertices. The minimum number of brushes required for cleaning the network D is called its brush number. The tattooing of a simple connected directed graph D is a particular type of the cleaning in which an arc are coloured by the colour of the colour-brush transiting it and the tattoo number of D is a corresponding derivative of brush numbers in it. Tattooing along an out-arc of a vertex v may proceed if a minimum set of colour-brushes is allocated (primary colours) or combined with those which have arrived (including colour blends) together with mutation of permissible new colour blends, has cardinality greater than or equal to dG+v. 2020 World Scientific Publishing Company.

Source

Journal of Interconnection Networks, Vol-20, No. 2

Date

2020-01-01

Publisher

World Scientific

Subject

colour-brushes; friendship graph; J 9-graphs; Joost graph; primary colour; tattoo number; Tattooing of graphs

Coverage

Kok J., Department of Mathematics, CHRIST (Deemed to Be University), Bangalore, 560029, India; Naduvath S., Department of Mathematics, CHRIST (Deemed to Be University), Bangalore, 560029, India

Rights

All Open Access; Green Open Access

Relation

ISSN: 2192659

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.1142/S0219265920500061

https://www.scopus.com/inward/record.uri?eid=2-s2.0-85092326254&doi=10.1142%2fS0219265920500061&partnerID=40&md5=8053d8926695bc7ebc43a48ee00d84bb