کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8897661 1631038 2018 33 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Signed bicyclic graphs minimizing the least Laplacian eigenvalue
ترجمه فارسی عنوان
نمودارهای دوچرخهسواری را امضا کرده و حداقل مقدار خاصی از لاپلایس را به حداقل می رساند
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی
A signed graph is a pair Γ=(G,σ), where G=(V(G),E(G)) is a graph and σ:E(G)→{+1,−1} is the sign function on the edges of G. For a signed graph we consider the Laplacian matrix defined as L(Γ)=D(G)−A(Γ), where D(G) is the matrix of vertices degrees of G and A(Γ) is the (signed) adjacency matrix. The least Laplacian eigenvalue is zero if and only if the signed graph is balanced, i.e. all cycles contain an even number of negative edges. Here we show that among the unbalanced bicyclic signed graphs of given order n≥5 the least Laplacian eigenvalue is minimal for signed graphs consisting of two triangles, only one of which is unbalanced, connected by a path. We also identify the signed graphs minimizing the least eigenvalue among those whose unbalanced (bicyclic) base is a theta-graph.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 557, 15 November 2018, Pages 201-233
نویسندگان
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