Abstract
Let k be a positive integer. An adjacent vertex distinguishing (for short, AVD) totalk-coloring ϕ of a graph G is a proper total k-coloring of G such that no pair of adjacent vertices have the same set of colors, where the set of colors at a vertex v is {ϕ(v)}∪{ϕ(e):e is incident to v}. Zhang et al. conjectured in 2005 that every graph with maximum degree Δ has an AVD total (Δ+3)-coloring. Recently, Papaioannou and Raftopoulou confirmed the conjecture for 4-regular graphs. In this paper, by applying the Combinatorial Nullstellensatz, we verify the conjecture for all graphs with maximum degree 4.
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.
