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| Regular and Maximal Graphs with Prescribed Tripartite Graph as a Star Complement* |
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Citation： |
Xiaona FANG,Lihua YOU.Regular and Maximal Graphs with Prescribed Tripartite Graph as a Star Complement*[J].Chinese Annals of Mathematics B,2023,44(4):517~532 |
| Page view： 1221
Net amount： 672 |
Authors： |
Xiaona FANG; Lihua YOU |
Foundation： |
This work was supported by the National Natural Science Foundation of China (No. 11971180, 12271337)and the Guangdong Provincial Natural Science Foundation (No. 2019A1515012052). |
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| Abstract： |
Let G be a graph of order n and μ be an adjacency eigenvalue of G with multiplicity k ≥ 1. A star complement H for μ in G is an induced subgraph of G of order n - k with no eigenvalue μ, and the subset X = V (G - H) is called a star set for μ in G. The star complement provides a strong link between graph structure and linear algebra. In this paper, the authors characterize the regular graphs with K2,2,s (s ≥ 2) as a star complement for all possible eigenvalues, the maximal graphs with K2,2,s as a star complement for the eigenvalue μ = 1, and propose some questions for further research. |
Keywords： |
Adjacency eigenvalue, Star set, Star complement, Regular graph,Maximal graph |
Classification： |
05C50 |
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