JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (6): 44-55.doi: 10.6040/j.issn.1671-9352.0.2022.649

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Adjacent vertex reducible total labeling of unicyclic graphs

Li WANG(),Jingwen LI*(),Wenzhu YANG,Huayan PEI   

  1. School of Electronic and Information Engineering, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Received:2022-12-27 Online:2024-06-20 Published:2024-06-17
  • Contact: Jingwen LI E-mail:1175133725@qq.com;lijingwen28@163.com

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Abstract:

A new heuristic search algorithm is designed for the labeling problem of unicyclic transport networks in special scenarios, drawing on the ideas of intelligent algorithms, which can discriminate whether there is an adjacent vertex reducible total labeling for all unicyclic graphs within a finite number of vertices. Through experimental analysis of the set of unicyclic graphs, the labeling properties of several types of unicyclic graphs are found, several theorems are obtained, and a conjecture is given: All unicyclic graphs are AVRTL graphs.

Key words: unicyclic graph, adjacent vertex reducible total labeling, labeling algorithm, joint graph

CLC Number: 

  • O157.5

Fig.1

S4↑C8 and S5↓C6"

Fig.2

SUN7, 2 and (8, 5)-K"

Fig.3

The examples of AVRTL"

Fig.4

Cn "

Fig.5

Cn's labeling result graphs"

Fig.6

(n, t)-K"

Fig.7

SUNn, m"

Fig.8

Sm↑Cn"

Fig.9

(n, t)-K↑Pm"

Fig.10

Sn↓Cm"

1 ROSAA.On certain valuations of the vertices of a graph[J].Theory of Graphs,1967,1967,349-355.
2 KOTZIGA,ROSAA.Magic valuations of finite graphs[J].Canadian Mathematical Bulletin,1970,13(4):451-461.
doi: 10.4153/CMB-1970-084-1
3 MACDOUGALLJ A,MILLERM,WALLISW D.Vertex-magic total labeling of graphs[J].Utilitas Mathematics,2002,61,3-21.
4 BURRIS A C. Vertex-distinguishing edge-colorings[D]. Memphis: Memphis State University, 1993: 1-9.
5 BALISTERP N,RIORDANO M,SCHELPR H.Vertex-distinguishing edge coloring of graphs[J].Graph Theory,2003,42(2):95-109.
doi: 10.1002/jgt.10076
6 ZHANGZhongfu,LIULinzhong,WANGJianfang.Adjacent strong edge coloring of graphs[J].Applied Mathematics Letters,2002,15(5):623-626.
doi: 10.1016/S0893-9659(02)80015-5
7 ZHANGZhongfu,CHENXiang'en,LIJingwen,et al.On adjacent vertex distinguishing total coloring of graphs[J].Science in China Series A: Mathematics,2005,48(3):289-299.
doi: 10.1360/03YS0207
8 ZHANGZhongfu,LIJingwen.D(β)-vertex distinguishing edge coloring of graphs[J].Journal of Mathematics,2006,49(3):703-708.
9 ZHANGZhongfu,LIJingwen,CHENXiang'en,et al.D(β)-vertex distinguishing total coloring of graphs[J].Science in China Series A: Mathematics,2006,49(10):1430-1440.
doi: 10.1007/s11425-006-2029-x
10 ZHANGZhongfu,QIUPengxiang,XUBaogen,et al.Vertex distinguishing total coloring of graphs[J].ARS Combinatoria,2008,87(2):33-45.
11 LI Jingwen, ZHANG Zhongfu, ZHU Enqiang, et al. Adjacent vertex reducible edge-total coloring of graphs[C]// 2009 2nd International Conference on Biomedical Engineering and Informatics. New York: IEEE Press, 2009: 1-3.
12 张园萍,强会英,孙亮萍.星扇轮联图的邻点可约边染色[J].数学的实践与认识,2012,42(13):207-213.
doi: 10.3969/j.issn.1000-0984.2012.13.030
ZHANGYuanping,QIANGHuiying,SUNLiangping.Adjacent reducible edge coloring of star fan wheel of joint-graphs[J].Mathematics in Practice and Theory,2012,42(13):207-213.
doi: 10.3969/j.issn.1000-0984.2012.13.030
13 王笔美,李敬文,顾彦波,等.单圈图的边幻和全标号[J].山东大学学报(理学版),2020,55(9):42-50.
WANGBimei,LIJingwen,GUYanbo,et al.Edge-magic total labeling of unicyclic graphs[J].Journal of Shandong University (Natural Science),2020,55(9):42-50.
14 罗榕,李敬文,张树成,等.若干联图的邻点和可约边染色[J].华中师范大学学报(自然科学版),2023,57(2):201-207.
LUORong,LIJingwen,ZHANGShucheng,et al.Adjacent points sum reducible edge coloring of some joint graphs[J].Journal of Central China Normal University (Natural Sciences),2023,57(2):201-207.
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