Nullity and Bounds to the Nullity of Dendrimer Graphs
نویسندگان
چکیده
منابع مشابه
On the nullity of graphs
The nullity of a graph G, denoted by η(G), is the multiplicity of the eigenvalue zero in its spectrum. It is known that η(G) ≤ n − 2 if G is a simple graph on n vertices and G is not isomorphic to nK1. In this paper, we characterize the extremal graphs attaining the upper bound n− 2 and the second upper bound n− 3. The maximum nullity of simple graphs with n vertices and e edges, M(n, e), is al...
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The nullity of a graph G, denoted by η(G), is the multiplicity of the eigenvalue zero in its spectrum. It is known that η(G) ≤ n − 2 if G is a simple graph on n vertices and G is not isomorphic to nK1. In this paper, we characterize the extremal graphs attaining the upper bound n− 2 and the second upper bound n− 3. The maximum nullity of simple graphs with n vertices and e edges, M(n, e), is al...
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The rank+nullity theorem states that, if T is a linear transformation from a finite-dimensional vector space V to a finite-dimensional vector space W , then dim(V ) = rank(T ) + nullity(T ), where rank(T ) = dim(im(T )) and nullity(T ) = dim(ker(T )). The proof treated here is standard; see, for example, [14]: take a basis A of ker(T ) and extend it to a basis B of V , and then show that dim(im...
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The spectrum of a graph G is the set of eigenvalues of the 0–1 adjacency matrix of G. The nullity of a graph is the number of zeros in its spectrum. It is shown that the nullity of the line graph of a tree is at most one. c © 2001 Elsevier Science B.V. All rights reserved.
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Combinatorial matrix theory, which involves connections between linear algebra, graph theory, and combinatorics, is a vital area and dynamic area of research, with applications to fields such as biology, chemistry, economics, and computer engineering. One area generating considerable interest recently is the study of the minimum rank of matrices associated with graphs. Let F be any field. For a...
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ژورنال
عنوان ژورنال: AL-Rafidain Journal of Computer Sciences and Mathematics
سال: 2013
ISSN: 2311-7990
DOI: 10.33899/csmj.2013.163548