caa a22 4500 605462224 CHVBK 20210128100247.0 cr unu---uuuuu 210128e20150201xx s 000 0 eng 10.1007/s10114-015-4114-y doi (NATIONALLICENCE)springer-10.1007/s10114-015-4114-y Neighbor sum distinguishing total colorings of triangle free planar graphs [Elektronische Daten] [Ji Wang, Qiao Ma, Xue Han] A total k-coloring c of a graph G is a proper total coloring c of G using colors of the set [k] = {1, 2, ..., k}. Let f(u) denote the sum of the color on a vertex u and colors on all the edges incident to u. A k-neighbor sum distinguishing total coloring of G is a total k-coloring of G such that for each edge uv ∈ E(G), f(u) ≠ f(v). By χ″nsd(G), we denote the smallest value k in such a coloring of G. Pilśniak and Woźniak conjectured that χ″nsd(G) ≤ Δ(G)+3 for any simple graph with maximum degree Δ(G). In this paper, by using the famous Combinatorial Nullstellensatz, we prove that the conjecture holds for any triangle free planar graph with maximum degree at least 7. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 Neighbor sum distinguishing total coloring nationallicence combinatorial Nullstellensatz nationallicence triangle free planar graph nationallicence Wang Ji School of Mathematical Sciences, University of Ji'nan, 250022, Ji'nan, P. R. China aut Ma Qiao School of Mathematical Sciences, University of Ji'nan, 250022, Ji'nan, P. R. China aut Han Xue School of Mathematical Sciences, University of Ji'nan, 250022, Ji'nan, P. R. China aut Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/2(2015-02-01), 216-224 1439-8516 31:2<216 2015 31 10114 https://doi.org/10.1007/s10114-015-4114-y text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10114-015-4114-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Wang Ji School of Mathematical Sciences, University of Ji'nan, 250022, Ji'nan, P. R. China aut NATIONALLICENCE 700 1- Ma Qiao School of Mathematical Sciences, University of Ji'nan, 250022, Ji'nan, P. R. China aut NATIONALLICENCE 700 1- Han Xue School of Mathematical Sciences, University of Ji'nan, 250022, Ji'nan, P. R. China aut NATIONALLICENCE 773 0- Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/2(2015-02-01), 216-224 1439-8516 31:2<216 2015 31 10114