کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8898070 | 1631057 | 2018 | 19 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The rank of a signed graph in terms of the rank of its underlying graph
ترجمه فارسی عنوان
رتبه یک نمودار امضایی از لحاظ رتبه گرافیکی پایه آن
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
Let Î=(G,Ï) be a signed graph and A(Î) be its adjacency matrix, where G is the underlying graph of Î. The rank r(Î) of Î is the rank of A(Î). We know that for a signed graph Î=(G,Ï), Î is balanced if and only if Î=(G,Ï)â¼(G,+). That is, when Î is balanced, then r(Î)=r(G), where r(G) is the rank of the underlying graph G of Î. A natural problem is that: how about the relations between the rank of an unbalanced signed graph and the rank of its underlying graph? In this paper, we first prove that r(G)â2d(G)â¤r(Î)â¤r(G)+2d(G) for an unbalanced signed graph with d(G)â¥1, where d(G)=|E(G)|â|V(G)|+Ï(G) is the dimension of cycle spaces of G, Ï(G) is the number of connected components of G. As an application, we also prove that 1âd(G)
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 538, 1 February 2018, Pages 166-186
Journal: Linear Algebra and its Applications - Volume 538, 1 February 2018, Pages 166-186
نویسندگان
Yong Lu, Ligong Wang, Qiannan Zhou,