Relations between degrees, conjugate degrees and graph energies

详细信息    查看全文

• 作者：Kinkar Ch. Das^a ; ^{kinkardas2003@googlemail.com} ; Seyed Ahmad Mojallal^a ; ^{ahmad_mojalal@yahoo.com} ; Ivan Gutman^b ; ^c ; ^{gutman@kg.ac.rs}
• 关键词：05C50 ; 05C07
• 刊名：Linear Algebra and its Applications
• 出版年：2017
• 出版时间：15 February 2017
• 年：2017
• 卷：515
• 期：Complete
• 页码：24-37
• 全文大小：319 K
• 卷排序：515

文摘

Let G be a simple graph of order n with maximum degree Δ and minimum degree δ  . Let (d)=(d1,d2,…,dn)(d)=(d1,d2,…,dn) and (d⁎)=(d1⁎,d2⁎,…,dn⁎) be the sequences of degrees and conjugate degrees of G  . We define π=∑i=1ndi and π⁎=∑i=1ndi⁎, and prove that π⁎≤LEL≤IE≤ππ⁎≤LEL≤IE≤π where LEL and IE are, respectively, the Laplacian-energy-like invariant and the incidence energy of G  . Moreover, we prove that π−π⁎>(δ/2)(n−Δ) for a certain class of graphs. Finally, we compare the energy of G and π, and present an upper bound for the Laplacian energy in terms of degree sequence.