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pro vyhledávání: '"Koolen A"'
Autor:
Lv, Chenhui, Koolen, Jack H.
Let $\Gamma$ be a distance-regular graph with classical parameters $(D, b, \alpha, \beta)$ satisfying $b\geq 2$ and $D\geq 3$. Let $r=1+b+b^2+\cdots+b^{D-1}$. In 1999, K. Metsch showed that there exists a positive constant $C(\alpha,b)$ only dependin
Externí odkaz:
http://arxiv.org/abs/2410.22994
Acceleration for non-convex functions has been an important problem in optimisation. We revisit star-convex functions, which are strictly unimodal on all lines through a minimizer. In [1], the authors accelerate gradient descent for star-convex funct
Externí odkaz:
http://arxiv.org/abs/2405.18976
Let $\Gamma$ be a graph with diameter at least two. Then $\Gamma$ is said to be $1$-homogeneous (in the sense of Nomura) whenever for every pair of adjacent vertices $x$ and $y$ in $\Gamma$, the distance partition of the vertex set of $\Gamma$ with r
Externí odkaz:
http://arxiv.org/abs/2404.01134
An association scheme is called amorphic if every possible fusion of relations gives rise to a fusion scheme. We call a pair of relations fusing if fusing that pair gives rise to a fusion scheme. We define the fusing-relations graph on the set of rel
Externí odkaz:
http://arxiv.org/abs/2404.00567
Autor:
Yang, Qianqian, Koolen, Jack H.
In this paper we will give a structure theory for regular graphs with fixed smallest eigenvalue. As a consequence of this theory, we show that a $k$-regular graph with smallest eigenvalue $-\lambda$ has clique number linear in $k$ if $k$ is large wit
Externí odkaz:
http://arxiv.org/abs/2401.10468
In this paper we study when the $q$-distance matrix of a distance-regular graph has few distinct eigenvalues. We mainly concentrate on diameter 3.
Comment: 15 pages
Comment: 15 pages
Externí odkaz:
http://arxiv.org/abs/2401.05640
Publikováno v:
Electron. J. Combin. 31(2) (2024), #P2.25
Let $\Gamma$ denote a distance-regular graph with diameter $D\geq 3$. Juri\v{s}i\'c and Vidali conjectured that if $\Gamma$ is tight with classical parameters $(D,b,\alpha,\beta)$, $b\geq 2$, then $\Gamma$ is not locally the block graph of an orthogo
Externí odkaz:
http://arxiv.org/abs/2312.05595
In this paper, we classify non-geometric distance-regular graphs of diameter at least $3$ with smallest eigenvalue at least $-3$. This is progress towards what is hoped to be an eventual complete classification of distance-regular graphs with smalles
Externí odkaz:
http://arxiv.org/abs/2311.09001
Local learning rules in biological neural networks (BNNs) are commonly referred to as Hebbian learning. [26] links a biologically motivated Hebbian learning rule to a specific zeroth-order optimization method. In this work, we study a variation of th
Externí odkaz:
http://arxiv.org/abs/2311.03483
In this paper, we study the $q$-distance matrix for a distance-regular graph and show that the $q$-distance matrix of a distance-regular graph with classical parameters ($D, q, \alpha, \beta$) has exactly three distinct eigenvalues, of which one is z
Externí odkaz:
http://arxiv.org/abs/2305.14636