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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 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 Pfaffian transform.

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

Journal of Integer Sequences [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 × 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 × n all ones matrix. For an m × n Boolean matrix M , its Boolean rank b ( M ) is the smallest positive integer b such that M = A B for some m × b Boolean matrix A and b × n Boolean matrix B . In 2009, M. Akelbek, S. Fital, and J. Shen gave an upper bound on the scrambling index of an n × n primitive matrix M in terms of its Boolean rank b ( M ) , and they also characterized all primitive...

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 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...

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