کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4601131 1336876 2012 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
The characteristic polynomial and the matchings polynomial of a weighted oriented graph
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
The characteristic polynomial and the matchings polynomial of a weighted oriented graph
چکیده انگلیسی

Let GσGσ be a weighted oriented graph with skew adjacency matrix S(Gσ)S(Gσ). Then GσGσ is usually referred as the weighted oriented graph associated to S(Gσ)S(Gσ). Denote by ϕ(Gσ;λ)ϕ(Gσ;λ) the characteristic polynomial of the weighted oriented graph GσGσ, which is defined asϕ(Gσ;λ)=det(λIn-S(Gσ))=∑i=0nai(Gσ)λn-i.In this paper, we begin by interpreting all the coefficients of the characteristic polynomial of an arbitrary real skew symmetric matrix in terms of its associated oriented weighted graph. Then we establish recurrences for the characteristic polynomial and deduce a formula on the matchings polynomial of an arbitrary weighted graph. In addition, some miscellaneous results concerning the number of perfect matchings and the determinant of the skew adjacency matrix of an unweighted oriented graph are given.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 436, Issue 9, 1 May 2012, Pages 3597–3607
نویسندگان
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