Name
Abstract | ||
|---|---|---|
The power index \(\Theta (\Gamma )\) of a graph \(\Gamma \) is the least order of a group G such that \(\Gamma \) can embed into the power graph of G. Furthermore, this group G is \(\Gamma \) -optimal if G has order \(\Theta (\Gamma )\). We say that \(\Gamma \) is power-critical if its order is equal to \(\Theta (\Gamma )\). This paper focuses on the power indices of complete graphs, complete bipartite graphs and 1-factors. We classify all power-critical graphs \(\Gamma '\) in these three families, and give a necessary and sufficient condition for \(\Gamma '\)-optimal groups. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1007/s00373-017-1851-y | Graphs and Combinatorics |
Keywords | Field | DocType |
Power graph, Embedding, Power index, Power-critical graph, 05C25 | Discrete mathematics,Graph,Combinatorics,Bipartite graph,Order (group theory),Mathematics | Journal |
Volume | Issue | ISSN |
33 | 5 | 0911-0119 |
Citations | PageRank | References |
1 | 0.36 | 8 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Xuanlong Ma | 1 | 13 | 3.42 |
| Min Feng | 2 | 4 | 1.96 |
| Kaishun Wang | 3 | 227 | 39.82 |