کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4599691 1631146 2014 18 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A reciprocal eigenvalue property for unicyclic weighted directed graphs with weights from {±1,±i}{±1,±i}
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
A reciprocal eigenvalue property for unicyclic weighted directed graphs with weights from {±1,±i}{±1,±i}
چکیده انگلیسی

A weighted directed graph is a directed graph G   whose underlying undirected graph is simple and whose edges have nonzero (directional) complex weights, that is, the presence of an edge (u,v)(u,v) of weight ww is as good as the presence of the edge (v,u)(v,u) with weight w¯, the complex conjugate of ww. Let G   be a weighted directed graph on vertices 1,2,…,n1,2,…,n. Denote by wuvwuv the weight of an edge (u,v)∈E(G)(u,v)∈E(G). The adjacency matrix A(G)A(G) of G   is an n×nn×n matrix with entries aij=wijaij=wij or w¯ji or 0, depending on whether (i,j)∈E(G)(i,j)∈E(G) or (j,i)∈E(G)(j,i)∈E(G) or otherwise, respectively. We supply a characterization of those unicyclic weighted directed graphs G   whose edges have weights from the set {±1,±i}{±1,±i} and whose adjacency matrix A(G)A(G) satisfies the following property: ‘λ   is an eigenvalue of A(G)A(G) with multiplicity k   if and only if 1/λ1/λ is an eigenvalue of A(G)A(G) with the same multiplicity’.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 449, 15 May 2014, Pages 417–434
نویسندگان
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