Neighbor full sum distinguishing total coloring of bicyclic graphs
LI Zhijun1， WEN Fei1， YANG Suiyi2
(1.Institute of Applied Mathematics， Lanzhou Jiaotong University， Lanzhou 730070， China；2.School of Mathematics and Statistics， Tianshui Normal University， Tianshui 741000， Gansu，China)
Abstract：Let f be a proper k-total coloring of G， and set (v)＝f(v)＋∑v∈e f(e)＋∑u∈N(v) f(u)， where N(v)＝{u∈V(G)|uv∈E(G)}. If (u)≠(v) for any edge uv∈E(G)， then f is called a k-neighbor full sum distinguishing total coloring of G. The minimum number k is called the neighbor full sum distinguishing total chromatic number of G and denoted by ftndiΣ(G). In this paper， the neighbor full sum distinguishing total coloring of bicyclic graphs is completely considered by applying structural analysis method， and it is obtained that ftndiΣ(G)＝Δ(G)＋1. Moreover， it further shows that the neighbor full sum distinguishing total coloring conjecture always holds on any bicyclic graph.
李志军,文 飞,杨随义. 双圈图的邻点全和可区别全染色[J]. 华中师范大学学报(自然科学版), 2025, 59(4): 568-576.
LI Zhijun,WEN Fei,YANG Suiyi. Neighbor full sum distinguishing total coloring of bicyclic graphs. journal1, 2025, 59(4): 568-576.
2025, Vol. 59 
