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On the lower bound of the sum of the algebraic connectivity of a graph and its complement
Journal of Combinatorial Theory Series B ( IF 1.2 ) Pub Date : 2021-06-30 , DOI: 10.1016/j.jctb.2021.06.007 Mostafa Einollahzadeh , Mohammad Mahdi Karkhaneei
中文翻译:
关于图及其补的代数连通性和的下界
更新日期:2021-06-30
Journal of Combinatorial Theory Series B ( IF 1.2 ) Pub Date : 2021-06-30 , DOI: 10.1016/j.jctb.2021.06.007 Mostafa Einollahzadeh , Mohammad Mahdi Karkhaneei
For a graph G, let denote its second smallest Laplacian eigenvalue. It was conjectured that , where is the complement of G. This conjecture has been proved for various families of graphs. Here, we prove this conjecture in the general case. Also, we will show that , where n is the number of vertices of G.
中文翻译:
关于图及其补的代数连通性和的下界
对于图G,让表示其第二小的拉普拉斯特征值。据推测,, 在哪里 是G的补码。这个猜想已经在各种图族中得到证明。在这里,我们在一般情况下证明这个猜想。此外,我们将证明,其中n是G的顶点数。