کد مقاله کد نشریه سال انتشار مقاله انگلیسی ترجمه فارسی نسخه تمام متن
6415985 1631084 2016 16 صفحه PDF سفارش دهید دانلود رایگان
عنوان انگلیسی مقاله ISI
Strong reciprocal eigenvalue property of a class of weighted graphs
ترجمه فارسی عنوان
اموال صحیح متقابل خاصی از یک کلاس از نمودارهای وزن
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موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

Let H be the class of connected bipartite graphs G with a unique perfect matching M. For GâH, let WG be the set of weight functions w on the edge set E(G) such that w(e)=1 for each matching edge and w(e)>0 for each nonmatching edge. Let Gw denote the weighted graph with GâH and wâWG. The graph Gw is said to satisfy the reciprocal eigenvalue property, property (R), if 1/Î» is an eigenvalue of the adjacency matrix A(Gw) whenever Î» is an eigenvalue of A(Gw). Moreover, if the multiplicities of the reciprocal eigenvalues are the same, we say Gw has the strong reciprocal eigenvalue property, property (SR). Let Hg={GâH|G/MÂ is bipartite}, where G/M is the graph obtained from G by contracting each edge in M to a vertex.Recently in [12], it was shown that if GâHg, then Gw has property (SR) for some wâWG if and only if Gw has property (SR) for each wâWG if and only if G is a corona graph (obtained from another graph H by adding a new pendant vertex to each vertex of H).Now we have the following questions. Is there a graph GâHâHg such that Gw has property (SR) for each wâWG? Are there graphs GâHâHg such that Gw never has property (SR), not even for one wâWG? Are there graphs GâH such that Gw has property (SR) for some wâWG but not for all wâWG? In this article, we supply answers to these three questions. We also supply a graph class larger than Hg where for any graph G, if Gw has property (SR) for one wâWG, then G is a corona graph.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 511, 15 December 2016, Pages 460-475
نویسندگان
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