کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4600811 | 1336864 | 2011 | 5 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Proof of conjecture involving the second largest signless Laplacian eigenvalue and the index of graphs
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
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چکیده انگلیسی
Let G = (V, E) be a simple graph. Denote by D(G) the diagonal matrix of its vertex degrees and by A(G) its adjacency matrix. Then the signless Laplacian matrix of G is Q(G) = D(G) + A(G ). In [5], Cvetković et al. have given the following conjecture involving the second largest signless Laplacian eigenvalue (q2q2) and the index (λ1λ1) of graph G (see also Aouchiche and Hansen [1]):1-n-1⩽q2-λ1⩽n-2-2n-4with equality if and only if G is the star K1,n-1K1,n-1 for the lower bound, and if and only if G is the complete bipartite graph Kn-2,2Kn-2,2 for the upper bound. In this paper we prove the lower bound and characterize the extremal graphs.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 435, Issue 10, 15 November 2011, Pages 2420–2424
Journal: Linear Algebra and its Applications - Volume 435, Issue 10, 15 November 2011, Pages 2420–2424
نویسندگان
Kinkar Ch. Das,