Forbidden subgraphs of power graphs
Date
02/07/2021Metadata
Show full item recordAbstract
The undirected power graph (or simply power graph) of a group G, denoted by P(G), is a graph whose vertices are the elements of the group G, in which two vertices u and v are connected by an edge between if and only if either u = vi or v = uj for some i,j. A number of important graph classes, including perfect graphs, cographs, chordal graphs, split graphs, and threshold graphs, can be defined either structurally or in terms of forbidden induced subgraphs. We examine each of these five classes and attempt to determine for which groups G the power graph P(G) lies in the class under consideration. We give complete results in the case of nilpotent groups, and partial results in greater generality. In particular, the power graph is always perfect; and we determine completely the groups whose power graph is a threshold or split graph (the answer is the same for both classes). We give a number of open problems.
Citation
Manna , P , Cameron , P J & Mehatari , R 2021 , ' Forbidden subgraphs of power graphs ' , Electronic Journal of Combinatorics , vol. 28 , no. 3 , P3.4 . https://doi.org/10.37236/9961
Publication
Electronic Journal of Combinatorics
Status
Peer reviewed
DOI
10.37236/9961ISSN
1097-1440Type
Journal article
Description
Funding: CSIR, India (Grant No-09/983(0037)/2019-EMR-I), SERB, India through Core Research Grant (File Number-CRG/2020/000447).Collections
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