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Displaying 481 – 500 of 546

The Minimum Spectral Radius of Signless Laplacian of Graphs with a Given Clique Number

Li Su, Hong-Hai Li, Jing Zhang (2014)

Discussiones Mathematicae Graph Theory

In this paper we observe that the minimal signless Laplacian spectral radius is obtained uniquely at the kite graph PKn−ω,ω among all connected graphs with n vertices and clique number ω. In addition, we show that the spectral radius μ of PKm,ω (m ≥ 1) satisfies [...] More precisely, for m > 1, μ satisfies the equation [...] where [...] and [...] . At last the spectral radius μ(PK∞,ω) of the infinite graph PK∞,ω is also discussed.

The Moore-Penrose inverse of a free matrix.

Britz, Thomas (2007)

ELA. The Electronic Journal of Linear Algebra [electronic only]

The nonnegative $P_{0}$ -matrix completion problem.

Choi, Ji Young, Dealba, Luz Maria, Hogben, Leslie, Kivunge, Benard M., Nordstrom, Sandra K., Shedenhelm, Mike (2003)

ELA. The Electronic Journal of Linear Algebra [electronic only]

The number of eigenvalues greater than two in the Laplacian spectrum of a graph

Merris, Russell (1991)

Portugaliae mathematica

The orderings of bicyclic graphs and connected graphs by algebraic connectivity.

Li, Jianxi, Guo, Ji-Ming, Shiu, Wai Chee (2010)

The Electronic Journal of Combinatorics [electronic only]

The $P_{0}$ -matrix completion problem.

Choi, Ji Young, DeAlba, Luz Maria, Hogben, Leslie, Maxwell, Mandi S., Wangsness, Amy (2002)

ELA. The Electronic Journal of Linear Algebra [electronic only]

The path is the tree with smallest greatest Laplacian eigenvalue

Miroslav Petrović, Ivan Gutman (2002)

Kragujevac Journal of Mathematics

The path polynomial of a complete graph.

da Fonseca, C. M. (2003)

ELA. The Electronic Journal of Linear Algebra [electronic only]

The permanent of the Laplacian matrix of a bipartite graph

Antonín Vrba (1986)

Czechoslovak Mathematical Journal

The Pfaffian transform.

Austin, Tracale, Bantilan, Hans, Egge, Eric S., Jonas, Isao, Kory, Paul (2009)

Journal of Integer Sequences [electronic only]

The P-Laplacian spectral radius of weighted trees with a degree sequence and a weight set.

Zhang, Guang-Jun, Zhang, Xiao-Dong (2011)

ELA. The Electronic Journal of Linear Algebra [electronic only]

The possible numbers of zeros in an orthogonal matrix.

Cheon, G.-S., Johnson, C.R., Lee, S.-G., Pribble, E.J. (1999)

ELA. The Electronic Journal of Linear Algebra [electronic only]

The primitive Boolean matrices with the second largest scrambling index by Boolean rank

Yan Ling Shao, Yubin Gao (2014)

Czechoslovak Mathematical Journal

The scrambling index of an $n \times n$ primitive Boolean matrix $A$ is the smallest positive integer $k$ such that $A^{k} {(A^{T})}^{k} = J$ , where $A^{T}$ denotes the transpose of $A$ and $J$ denotes the $n \times n$ all ones matrix. For an $m \times n$ Boolean matrix $M$ , its Boolean rank $b (M)$ is the smallest positive integer $b$ such that $M = A B$ for some $m \times b$ Boolean matrix $A$ and $b \times n$ Boolean matrix $B$ . In 2009, M. Akelbek, S. Fital, and J. Shen gave an upper bound on the scrambling index of an $n \times n$ primitive matrix $M$ in terms of its Boolean rank $b (M)$ , and they also characterized all primitive...

The $Q$ -matrix completion problem.

Dealba, Luz Maria, Hogben, Leslie, Sarma, Bhaba Kumar (2009)

ELA. The Electronic Journal of Linear Algebra [electronic only]

The Randić energy of generalized double sun

Wei Gao (2022)

Czechoslovak Mathematical Journal

We show that the family of trees defined as generalized double sun of odd order satisfies the conjecture for the Randić energy proposed by I. Gutman, B. Furtula, S. B. Bozkurt (2014).

The rank of a cograph.

Royle, Gordon F. (2003)

The Electronic Journal of Combinatorics [electronic only]

The real symmetric matrices of odd order with a P-set of maximum size

Zhibin Du, Carlos Martins da Fonseca (2016)

Czechoslovak Mathematical Journal

Suppose that $A$ is a real symmetric matrix of order $n$ . Denote by $m_{A} (0)$ the nullity of $A$ . For a nonempty subset $α$ of ${1, 2, ..., n}$ , let $A (α)$ be the principal submatrix of $A$ obtained from $A$ by deleting the rows and columns indexed by $α$ . When $m_{A (α)} (0) = m_{A} (0) + | α |$ , we call $α$ a P-set of $A$ . It is known that every P-set of $A$ contains at most $⌊ n / 2 ⌋$ elements. The graphs of even order for which one can find a matrix attaining this bound are now completely characterized. However, the odd case turned out to be more difficult to tackle. As a first step...

Currently displaying 481 – 500 of 546

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Displaying 481 – 500 of 546

The Minimum Spectral Radius of Signless Laplacian of Graphs with a Given Clique Number

The Moore-Penrose inverse of a free matrix.

The nonnegative $P_{0}$ -matrix completion problem.

The number of eigenvalues greater than two in the Laplacian spectrum of a graph

The orderings of bicyclic graphs and connected graphs by algebraic connectivity.

The $P_{0}$ -matrix completion problem.

The path is the tree with smallest greatest Laplacian eigenvalue

The path polynomial of a complete graph.

The permanent of the Laplacian matrix of a bipartite graph

The Pfaffian transform.

The P-Laplacian spectral radius of weighted trees with a degree sequence and a weight set.

The possible numbers of zeros in an orthogonal matrix.

The primitive Boolean matrices with the second largest scrambling index by Boolean rank

The $Q$ -matrix completion problem.

The Randić energy of generalized double sun

The rank of a cograph.

The real symmetric matrices of odd order with a P-set of maximum size

The scattering matrix of a graph.

The signless Laplacian separator of graphs.

The signless Laplacian spectral radius of bicyclic graphs with a given girth.

Currently displaying 481 – 500 of 546