Neighbor sum distinguishing total chromatic number of planar graphs

作者：Xu, Changqing^*; Li, Jianguo; Ge, Shan

来源：Applied Mathematics and Computation, 2018, 332: 189-196.

DOI：10.1016/j.amc.2018.03.013

• Neighbor sum distinguishing total chromatic number
• Combinatorial Nullstellensatz
• Planar graph

Let G = (V(G), E(G)) be a graph and phi be a proper k-total coloring of G. Set f(phi)(v) = Sigma(uv is an element of E(G)) phi(UV) + phi(V), for each v is an element of V (G). If f(phi)(u) not equal f(phi)(v) for each edge uv is an element of E(G), the coloring phi is called a k-neighbor sum distinguishing total coloring of G. The smallest integer k in such a coloring of G is the neighbor sum distinguishing total chromatic number, denoted by chi(Sigma)''(G). In this paper, by using the famous Combinatorial Nullstellensatz, we determine chi(Sigma)''(G) for any planar graph G with Delta(G)>= 13.

• 出版日期2018-9-1
• 单位河北工业大学