单圈图的邻点全和可区别全染色  

Neighbor Full Sum Distinguishing Total Coloring of Unicyclic Graph

作　　者：李志军 文飞[1] LI Zhijun;WEN Fei(Institute of Applied Mathematics,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学应用数学研究所,兰州730070

出　　处：《吉林大学学报（理学版）》2024年第3期497-502,共6页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11961041,12261055);甘肃省自然科学基金(批准号:21JR11RA135).

摘　　要：用结构分析法完整刻画单圈图U的邻点全和可区别全染色,并得到当U■C_(n)且n■0(mod 3)时,ftndiΣ(U)=Δ(U)+2;其他情况下,ftndiΣ(U)=Δ(U)+1.表明邻点全和可区别全染色猜想在任意单圈图上都成立.By using structural analysis method,we completely characterized the neighbor full sum distinguishing total coloring of unicyclic graph U,and obtained that ftndiΣ(U)=Δ(U)+2 when U■C_(n)and n■0(mod 3),ftndiΣ(U)=Δ(U)+1 in other cases.This result shows that the neighbor full sum distinguishing total coloring conjecture holds on any unicyclic graph.

关 键 词：单圈图 正常全染色 邻点全和可区别全染色 邻点全和可区别全色数 

分 类 号：O157.5[理学—数学]