Abstract
The neighbor-distinguishing total chromatic number χa′′(G) of a graph G is the smallest integer k such that G can be totally colored using k colors with a condition that any two adjacent vertices have different sets of colors. In this paper, we give a sufficient and necessary condition for a planar graph G with maximum degree 13 to have χa′′(G)=14 or χa′′(G)=15. Precisely, we show that if G is a planar graph of maximum degree 13, then 14≤χa′′(G)≤15; and χa′′(G)=15 if and only if G contains two adjacent 13-vertices.
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.
