JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (9): 42-50.doi: 10.6040/j.issn.1671-9352.0.2019.439

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Edge-magic total labeling of unicyclic graphs

WANG Bi-mei, LI Jing-wen*, GU Yan-bo, SHAO Shu-hong   

  1. School of Electronic and Information Engineering, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Published:2020-09-17

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Abstract: An edge-magic total labeling is a one-to-one mapping f from V(G)∪E(G) onto {1,2,…,p+q} such that there exists a constant K satisfying f(u)+f(v)+f(uv)=K, for each uv∈E(G). A graph G(p,q) which has a edge-magic total labeling can be called edge-magic total labeling graph. An algorithm to label the unicyclic graphs with less than 16 vertices is designed. The rules of two special unicyclic graphs are obtained, and CnSymbolQC@Sm and CnΔSm to describe the two types of graphs are defiened, and related theorems are given and proved. The results show that all the unicyclic graphs with less than or equal to 16 vertices have a edge-magic total labeling, and most of them are super edge-magic total labeling. Therefore, it is speculated that the unicyclic graphs with more than 16 vertices also have the same characters.

Key words: edge-magic total labeling, super edge-magic total labeling, unicyclic graph, algorithm

CLC Number: 

  • O157.5
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