| 摘要: |
| 设G是一个图，且 ，Nikiforov[1]将邻接矩阵和无符号拉普拉斯矩阵结合以便于统一地研究，即，其中分别表示图G的度矩阵和邻接矩阵。矩阵的谱半径叫作图G的α谱半径，关于α谱半径的谱Turán定理在[1]中已经给出。本文主要研究了完全多部图α谱半径在将一个顶点从一个部集移到另一个部集时的扰动性，并且给出用α谱Turán定理推导图的Turán定理的充分条件。 |
| 关键词: α谱半径 谱图兰定理 等同划分 完全多部图 |
| DOI： |
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| Perturbation of the α-spectral radius of complete multipartite graphs |
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Wu Yu-hao,Li Meng-yuan,Zhang Shan,Jin Ya-lei
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Mathematics and Science College,Shanghai Normal University
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| Abstract: |
| Let G be a graph and α∈[0,1), Nikiforov [17] merges the adjacency matrix and the signless laplacian matrix to A_α (G)=αD(G)+(1-α)A(G) in order to study them uniformly, where D(G),A(G) are the degree diagonal matrix and the adjacency matrix of G, respectively. The spectral radius of A_α (G) is called by α-spectral radius of the graph G, the spectral Turán theorem in terms of the α-spectral radius of the graph are given in [17]. In this paper, we study the perturbation of the complete multipartite graphs when move a vertex from a part to other part of the complete multipartite graphs. Moreover, we give some conditions when the spectral Turán of graphs implies the Turán theorem of graphs. |
| Key words: α-spectral radius Spectral Turán theorem Equitable partition Complete multipartite graphs. |
