Abstract
A total k--coloring c of G is called k-neighbor sum distinguishing if for each edge uv, the sum of color of u and the colors of its incident edges is different from the sum of color of v and the colors of its incident edges. The smallest k is called the neighbor sum distinguishing total chromatic number. and first introduced this coloring and conjectured that the neighbor sum distinguishing total chromatic number of G is less than or equal to maximum degree of G add 3 for any simple graph. By using the Combinatorial Nullstellensatz and the discharging method, we prove that the conjecture holds for graphs with maximum degree at least 8 and maximum average degree less than 4.5.
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 callDisclaimer: 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.
