Open AccessThe diachromatic number of double star graph
Author(s) -
Nilamsari Kusumastuti,
Raventino,
Fransiskus Fran
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/2106/1/012024
Subject(s) - algorithm , artificial intelligence , computer science , graph , theoretical computer science
We are interested in the extension for the concept of complete colouring for oriented graph G → that has been proposed in many different notions by several authors (Edwards, Sopena, and Araujo-Pardo in 2013, 2014, and 2018, respectively). An oriented colouring is complete if for every ordered pair of colours, at least one arc in G → whose endpoints are coloured with these colours. The diachromatic number, dac ( G → ) , is the greatest number of colours in a complete oriented colouring. In this paper, we establish the formula of diachromatic numbers for double star graph, k 1 , n , n → , over all possible orientations on the graph. In particular, if d in ( u ) = 0 (resp. dout ( u ) = 0)and d in ( w i ) = 1 (resp. d out ( w 1 ) = 1) for all i , then dac ( k 1 , n , n → ) = ⌊ n ⌋ + 1 , where u is the internal vertex and w i , i ∈ {1,…, n }, is the pendant vertices of the digraph.