کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4598398 1631083 2017 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Edge perturbation on graphs with clusters: Adjacency, Laplacian and signless Laplacian eigenvalues
ترجمه فارسی عنوان
آشفتگی لبه در نمودار با خوشه مجاورت، لاپلاس و مقادیر ویژه لاپلاس بدون نشانه
کلمات کلیدی
مجاورت، لاپلاس و طیف لاپلاسین بدون نشانه نمودار؛ خوشه گراف؛ اتصال جبری؛ شاخص لاپلاسانی؛ شاخص وابستگی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

Let G be a simple undirected graph of order n. A cluster in G of order c and degree s  , is a pair of vertex subsets (C,S)(C,S), where C   is a set of cardinality |C|=c≥2|C|=c≥2 of pairwise co-neighbor vertices sharing the same set S of s neighbors. Assuming that the graph G   has k≥1k≥1 clusters (C1,S1),…,(Ck,Sk)(C1,S1),…,(Ck,Sk), consider a family of k   graphs H1,…,HkH1,…,Hk and the graph G(H1,…,Hk)G(H1,…,Hk) which is obtained from G   after adding the edges of the graphs H1,…,HkH1,…,Hk whose vertex set of each HjHj is identified with CjCj, for j=1,…,kj=1,…,k. The Laplacian eigenvalues of G(H1,…,Hk)G(H1,…,Hk) remain the same, independently of the graphs H1,…,HkH1,…,Hk, with the exception of |C1|+⋯+|Ck|−k|C1|+⋯+|Ck|−k of them. These new Laplacian eigenvalues are determined using a unified approach which can also be applied to the determination of a same number of adjacency and signless Laplacian eigenvalues when the graphs H1,…,HkH1,…,Hk are regular. The Faria's lower bound on the multiplicity of the Laplacian eigenvalue 1 of a graph with pendant vertices is generalized. Furthermore, the algebraic connectivity and the Laplacian index of G(H1,…,Hk)G(H1,…,Hk) remain the same, independently of the graphs H1,…,HkH1,…,Hk.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 512, 1 January 2017, Pages 113–128
نویسندگان
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