Zobrazeno 1 - 10
of 56
pro vyhledávání: '"Taniguchi, Tetsuji"'
In this paper, we show that every connected signed graph with smallest eigenvalue strictly greater than $-2$ and large enough minimum degree is switching equivalent to a complete graph. This is a signed analogue of a theorem of Hoffman. The proof is
Externí odkaz:
http://arxiv.org/abs/2003.05578
As a natural generalization of line graphs, Hoffman line graphs were defined by Woo and Neumaier. Especially, Hoffman line graphs are closely related to the smallest eigenvalue of graphs, and the uniqueness of strict covers of a Hoffman line graph pl
Externí odkaz:
http://arxiv.org/abs/2002.08049
Publikováno v:
Quantum Inf Process 20, 95 (2021)
We propose a quantum walk defined by digraphs (mixed graphs). This is like Grover walk that is perturbed by a certain complex-valued function defined by digraphs. The discriminant of this quantum walk is a matrix that is a certain normalization of ge
Externí odkaz:
http://arxiv.org/abs/1910.12536
Publikováno v:
Linear Algebra and its Applications 466 (2015) 501-511
In this paper, we study the characteristic polynomials of the line graphs of generalized Bethe trees. We give an infinite family of such graphs sharing the same smallest eigenvalue. Our family generalizes the family of coronas of complete graphs disc
Externí odkaz:
http://arxiv.org/abs/1405.3475
Publikováno v:
J. Combin. Theory, Ser. B 110 (2015), pp. 90--111
We give a structural classification of edge-signed graphs with smallest eigenvalue greater than -2. We prove a conjecture of Hoffman about the smallest eigenvalue of the line graph of a tree that was stated in the 1970s. Furthermore, we prove a more
Externí odkaz:
http://arxiv.org/abs/1309.5178
In this paper, we introduce the notion of reproducing kernel Hilbert spaces for graphs and the Gram matrices associated with them. Our aim is to investigate the Gram matrices of reproducing kernel Hilbert spaces. We provide several bounds on the entr
Externí odkaz:
http://arxiv.org/abs/1212.4346
Publikováno v:
Discrete Applied Mathematics 176 (2014) 78-88
In this paper, we give a combinatorial characterization of the special graphs of fat Hoffman graphs containing $\mathfrak{K}_{1,2}$ with smallest eigenvalue greater than -3, where $\mathfrak{K}_{1,2}$ is the Hoffman graph having one slim vertex and t
Externí odkaz:
http://arxiv.org/abs/1211.3929
Publikováno v:
In Linear Algebra and Its Applications 15 October 2019 579:217-236
Publikováno v:
Ars Mathematica Contemporanea 7 (2014) 247-262
In this paper, we show that all fat Hoffman graphs with smallest eigenvalue at least -1-\tau, where \tau is the golden ratio, can be described by a finite set of fat (-1-\tau)-irreducible Hoffman graphs. In the terminology of Woo and Neumaier, we mea
Externí odkaz:
http://arxiv.org/abs/1111.7284
We investigate fat Hoffman graphs with smallest eigenvalue at least -3, using their special graphs. We show that the special graph S(H) of an indecomposable fat Hoffman graph H is represented by the standard lattice or an irreducible root lattice. Mo
Externí odkaz:
http://arxiv.org/abs/1110.6821