On the Baer-Lovasz-Tutte construction of groups from graphs: Isomorphism types and homomorphism notions

doi:10.1016/j.ejc.2021.103404

	On the Baer-Lovasz-Tutte construction of groups from graphs: Isomorphism types and homomorphism notions
	He, Xiaoyu 1,3; Qiao, Youming 2
刊名	EUROPEAN JOURNAL OF COMBINATORICS
	2021-12-01
卷号	98 页码:12
ISSN号	0195-6698
DOI	10.1016/j.ejc.2021.103404
英文摘要	Let p be an odd prime. From a simple undirected graph G, through the classical procedures of Baer (1938), Tutte (1947) and Lovasz (1989), there is a p-group PG of class 2 and exponent p that is naturally associated with G. Our first result is to show that this construction of groups from graphs respects isomorphism types. That is, given two graphs G and H, G and H are isomorphic as graphs if and only if PG and PH are isomorphic as groups. Our second contribution is a new homomorphism notion for graphs. Based on this notion, a category of graphs can be defined, and the Baer-Lovasz-Tutte construction naturally leads to a functor from this category of graphs to the category of groups. (c) 2021 Elsevier Ltd. All rights reserved.
资助项目	National Natural Science Foundation of China[61832003] ; National Natural Science Foundation of China[61761136014] ; National Natural Science Foundation of China[61872334] ; Strategic Priority Research Program of Chinese Academy of Sciences[XDA27000000] ; 973 Program of China[2016YFB1000201] ; K. C. Wong Education Foundation, China ; Australian Research Council[DP200100950]
WOS研究方向	Mathematics
语种	英语
出版者	ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
WOS记录号	WOS:000690737400007
内容类型	期刊论文
源URL	[http://119.78.100.204/handle/2XEOYT63/17087]
专题	中国科学院计算技术研究所
通讯作者	He, Xiaoyu
作者单位	1.Univ Chinese Acad Sci, Beijing, Peoples R China 2.Univ Technol Sydney, Ctr Quantum Software & Informat, Sydney, NSW, Australia 3.Chinese Acad Sci, Inst Comp Technol, Beijing, Peoples R China
推荐引用方式 GB/T 7714	He, Xiaoyu,Qiao, Youming. On the Baer-Lovasz-Tutte construction of groups from graphs: Isomorphism types and homomorphism notions[J]. EUROPEAN JOURNAL OF COMBINATORICS,2021,98:12.
APA	He, Xiaoyu,&Qiao, Youming.(2021).On the Baer-Lovasz-Tutte construction of groups from graphs: Isomorphism types and homomorphism notions.EUROPEAN JOURNAL OF COMBINATORICS,98,12.
MLA	He, Xiaoyu,et al."On the Baer-Lovasz-Tutte construction of groups from graphs: Isomorphism types and homomorphism notions".EUROPEAN JOURNAL OF COMBINATORICS 98(2021):12.