Neighbor Full Sum Distinguishing Total Coloring of Planar Graphs with Girth at Least 5
Zhongzheng Yue, Fei Wen · Axioms · 2025
A neighbor full sum distinguishing total coloring of a graph G is a proper k-total coloring ϕ such that no two adjacent vertices u and v satisfy ω(u)≠ω(v), where ω(v)=ϕ(v)+∑e∋vϕ(e)+∑u∈N(v)ϕ(u) and N(v)={u|uv∈E(G)}. The minimum positive integer k is called the neighbor full sum distinguishing total coloring of G, or ftndiΣ(G) for short. In this article, we verify that for a normal planar graph G, ftndiΣ(G)≤Δ(G)+3 if g(G)≥5 and Δ(G)≥22, which extends the result of Yue, et al. by reducing the girth condition from 6 to 5.