The underlying graph of a line digraph
نویسندگان
چکیده
منابع مشابه
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15 صفحه اولAlgebraic properties of a digraph and its line digraph
Let G be a digraph, LG its line digraph and A(G) and A(LG) their adjacency matrices. We present relations between the Jordan Normal Form of these two matrices. Besides, we study the spectra of those matrices and obtain a relationship between their characteristic polynomials that allows to relate properties of G and LG regarding the number of cycles of a given length.
متن کاملA characterization of the adjacency matrix of the line digraph of a regular digraph
A characterization of the adjacency matrix of the line digraph of a regular digraph is given. Some corollaries are observed.
متن کاملOn the structure of the adjacency matrix of the line digraph of a regular digraph
We show that the adjacency matrix M of the line digraph of a d-regular digraph D on n vertices can be written as M = AB, where the matrix A is the Kronecker product of the all-ones matrix of dimension d with the identity matrix of dimension n and the matrix B is the direct sum of the adjacency matrices of the factors in a dicycle factorization of D.
متن کاملThe underlying line digraph structure of some (0, 1)-matrix equations
From the theory of Ho0man polynomial, it is known that the adjacency matrix A of a strongly connected regular digraph of order n satis3es certain polynomial equation AP(A)=Jn, where l is a nonnegative integer, P(x) is a polynomial with rational coe5cients, and Jn is the n×n matrix of all ones. In this paper we present some su5cient conditions, in terms of the coe5cients of P(x), to ensure that ...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1992
ISSN: 0166-218X
DOI: 10.1016/0166-218x(92)90156-5