2-Distance sum distinguishing total coloring of Halin graphs
WANG Tongxin1， YANG Chao1， YIN Zhixiang1， YAO Bing2
(1.School of Mathematics， Physics and Statistics， Center of Intelligent Computing and Applied Statistics， Shanghai University of Engineering Science， Shanghai 201620， China；2.College of Mathematics and Statistics， Northwest Normal University， Lanzhou 730070， China)
Abstract：Let [k]＝{1,2，…， k} be a color set. Let f：V(G)∪E(G)→[k] be a k-total coloring of G. Set S(u)＝f(u)＋∑uf(uv)，where NG(u) is the neighbor set of vertex u. If S(u)≠S(v) for any two vertices u，v with their distance is not more than 2， then f is called the 2-distance sum distinguishing k-total coloring of G. The smallest value k that G admits a 2-distance sum distinguishing k-total coloring of G is called the 2-distance sum distinguishing total chromatic number of G， and denoted by χ″2－(G). By using Combinatorial Nullstellensatz， it is proved that χ″2－(G)≤max{Δ(G)＋2,9} for Halin graph G with maximum degree Δ(G)≥4.
2024, Vol. 58 
