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"

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