Abstract
The neighbourhood heterochromatic number nh c ( G ) of a non-empty graph G is the smallest integer l such that for every colouring of G with exactly l colours, G contains a vertex all of whose neighbours have different colours. We prove that lim n → ∞ ( nh c ( G n ) - 1 ) / | V ( G n ) | = 1 for any connected graph G with at least two vertices. We also give upper and lower bounds for the neighbourhood heterochromatic number of the 2 n -dimensional hypercube.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callSimilar Papers
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
