A note on minimum rank and maximum nullity of sign patterns.
Displaying 21 – 40 of 546
A note on the largest eigenvalue of non-regular graphs.
Liu, Bolian, Li, Gang (2008)
ELA. The Electronic Journal of Linear Algebra [electronic only]
A Note on the Permanental Roots of Bipartite Graphs
Heping Zhang, Shunyi Liu, Wei Li (2014)
Discussiones Mathematicae Graph Theory
It is well-known that any graph has all real eigenvalues and a graph is bipartite if and only if its spectrum is symmetric with respect to the origin. We are interested in finding whether the permanental roots of a bipartite graph G have symmetric property as the spectrum of G. In this note, we show that the permanental roots of bipartite graphs are symmetric with respect to the real and imaginary axes. Furthermore, we prove that any graph has no negative real permanental root, and any graph containing...
A note on tree realizations of matrices
Alain Hertz, Sacha Varone (2007)
RAIRO - Operations Research
It is well known that each tree metric M has a unique realization as a tree, and that this realization minimizes the total length of the edges among all other realizations of M. We extend this result to the class of symmetric matrices M with zero diagonal, positive entries, and such that mij + mkl ≤ max{mik + mjl, mil + mjk} for all distinct i,j,k,l.
A note on ultrametric matrices
Xiao-Dong Zhang (2004)
Czechoslovak Mathematical Journal
It is proved in this paper that special generalized ultrametric and special matrices are, in a sense, extremal matrices in the boundary of the set of generalized ultrametric and matrices, respectively. Moreover, we present a new class of inverse -matrices which generalizes the class of matrices.
A paintability version of the combinatorial Nullstellensatz, and list colorings of -partite -uniform hypergraphs.
Schauz, Uwe (2010)
The Electronic Journal of Combinatorics [electronic only]
A problem on matrices
V. de Valk (1989)
Compositio Mathematica
A quasi-spectral characterization of strongly distance-regular graphs.
Fiol, M.A. (2000)
The Electronic Journal of Combinatorics [electronic only]
A refinement of an inequality of Johnson, Loewy and London on nonnegative matrices and some applications.
Laffey, Thomas J., Meehan, Eleanor (1998)
ELA. The Electronic Journal of Linear Algebra [electronic only]
A relation between the multiplicity of the second eigenvalue of a graph Laplacian, Courant's nodal line theorem and the substantial dimension of tight polyhedral surfaces.
Tlusty, Tsvi (2007)
ELA. The Electronic Journal of Linear Algebra [electronic only]
A result related to the largest eigenvalue of a tree
Gurusamy Rengasamy Vijayakumar (2008)
Discussiones Mathematicae Graph Theory
In this note we prove that {0,1,√2,√3,2} is the set of all real numbers l such that the following holds: every tree having an eigenvalue which is larger than l has a subtree whose largest eigenvalue is l.
A sharp upper bound for the spectral radius of a nonnegative matrix and applications
Lihua You, Yujie Shu, Xiao-Dong Zhang (2016)
Czechoslovak Mathematical Journal
We obtain a sharp upper bound for the spectral radius of a nonnegative matrix. This result is used to present upper bounds for the adjacency spectral radius, the Laplacian spectral radius, the signless Laplacian spectral radius, the distance spectral radius, the distance Laplacian spectral radius, the distance signless Laplacian spectral radius of an undirected graph or a digraph. These results are new or generalize some known results.
A shorter proof of the distance energy of complete multipartite graphs
Wasin So (2017)
Special Matrices
Caporossi, Chasser and Furtula in [Les Cahiers du GERAD (2009) G-2009-64] conjectured that the distance energy of a complete multipartite graph of order n with r ≥ 2 parts, each of size at least 2, is equal to 4(n − r). Stevanovic, Milosevic, Hic and Pokorny in [MATCH Commun. Math. Comput. Chem. 70 (2013), no. 1, 157-162.] proved the conjecture, and then Zhang in [Linear Algebra Appl. 450 (2014), 108-120.] gave another proof. We give a shorter proof of this conjecture using the interlacing inequalities...
A simple proof of the Aztec diamond theorem.
Eu, Sen-Peng, Fu, Tung-Shan (2005)
The Electronic Journal of Combinatorics [electronic only]
A spectral bound for graph irregularity
Felix Goldberg (2015)
Czechoslovak Mathematical Journal
The imbalance of an edge in a graph is defined as , where is the vertex degree. The irregularity of is then defined as the sum of imbalances over all edges of . This concept was introduced by Albertson who proved that (where ) and obtained stronger bounds for bipartite and triangle-free graphs. Since then a number of additional bounds were given by various authors. In this paper we prove a new upper bound, which improves a bound found by Zhou and Luo in 2008. Our bound involves the...
A variant on the graph parameters of Colin de Verdière: implications to the minimum rank of graphs.
Barioli, Francesco, Fallat, Shaun, Hogben, Leslie (2005)
ELA. The Electronic Journal of Linear Algebra [electronic only]
About adjoint and -adjoint digraphs of -regular multigraphs. (Sobre digrafos adjuntos y adjuntos de multidigrafos -regulares.)
Osio, Elsa, Braicovich, Teresa, Bernardi, Cora, Costes, Cristina (2003)
Revista Colombiana de Matemáticas
Acyclic digraphs and eigenvalues of -matrices.
McKay, Brendan D., Oggier, Frédérique E., Royle, Gordon F., Sloane, N.J.A., Wanless, Ian M., Wilf, Herbert S. (2004)
Journal of Integer Sequences [electronic only]
Additive decomposition of matrices under rank conditions and zero pattern constraints
Harm Bart, Torsten Ehrhardt (2022)
Czechoslovak Mathematical Journal
This paper deals with additive decompositions of a given matrix , where the ranks of the summands are prescribed and meet certain zero pattern requirements. The latter are formulated in terms of directed bipartite graphs.
Adjacency matrix equations and related problems: Research notes
Maciej M. Sysło (1983)
Commentationes Mathematicae Universitatis Carolinae