Maximum Laplacian energy of unicyclic graphs

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• 作者：Kinkar Ch. Das^a ; ^{kinkardas2003@googlemail.com} ; Eliseu Fritscher^b ; ^{eliseu.fritscher@ufrgs.br} ; Lucé ; lia Kowalski Pinheiro^c ; ^{lucelia.kowalski@ufrgs.br} ; Vilmar Trevisan^c ; ^{trevisan@mat.ufrgs.br}
• 关键词：Unicyclic graph ; Laplacian matrix ; Laplacian energy ; Signless Laplacian energy
• 刊名：Discrete Applied Mathematics
• 出版年：2017
• 出版时间：19 February 2017
• 年：2017
• 卷：218
• 期：Complete
• 页码：71-81
• 全文大小：448 K
• 卷排序：218

文摘

We study the Laplacian and the signless Laplacian energy of connected unicyclic graphs, obtaining a tight upper bound for this class of graphs. We also find the connected unicyclic graph on nn vertices having largest (signless) Laplacian energy for 3≤n≤133≤n≤13. For n≥11n≥11, we conjecture that the graph consisting of a triangle together with n−3n−3 balanced distributed pendent vertices is the candidate having the maximum (signless) Laplacian energy among connected unicyclic graphs on nn vertices. We prove this conjecture for many classes of graphs, depending on σσ, the number of (signless) Laplacian eigenvalues bigger than or equal to 2.