کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8897867 | 1631047 | 2018 | 17 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Proof of conjecture involving algebraic connectivity and average degree of graphs
ترجمه فارسی عنوان
اثبات حدس است که شامل اتصال جبری و میانگین درجه گراف است
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
Let G be a simple connected graph of order n with m edges. Denote by D(G) the diagonal matrix of its vertex degrees and by A(G) its adjacency matrix. Then the Laplacian matrix of graph G is L(G)=D(G)âA(G). Among all eigenvalues of the Laplacian matrix L(G) of graph G, the most studied is the second smallest, called the algebraic connectivity a(G) of a graph. Let dâ¾(G) and δ(G) be the average degree and the minimum degree of graph G, respectively. In this paper we characterize all graphs for which (i) a(G)=1 with δ(G)â¥ânâ12â, and (ii)a(G)=2 with δ(G)â¥n2. In [1], Aouchiche mentioned a conjecture involving the algebraic connectivity a(G) and the average degree dâ¾(G) of graph G:a(G)âdâ¾(G)â¥4ânâ4n with equality holding if and only if Gâ¾â
K1,nâ2âªK1 (K1,nâ2 is a star of order nâ1 and Gâ¾ is the complement of graph G). Here we prove this conjecture.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 548, 1 July 2018, Pages 172-188
Journal: Linear Algebra and its Applications - Volume 548, 1 July 2018, Pages 172-188
نویسندگان
Kinkar Ch. Das,