Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8898070 | Linear Algebra and its Applications | 2018 | 19 Pages |
Abstract
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)
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Yong Lu, Ligong Wang, Qiannan Zhou,