Zobrazeno 1 - 10
of 296
pro vyhledávání: '"Koolen, Jack H."'
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 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
Graham and Lov\'{a}sz conjectured in 1978 that the sequence of normalized coefficients of the distance characteristic polynomial of a tree of order $n$ is unimodal with the maximum value occurring at $\lfloor\frac{n}{2}\rfloor$. In this paper we inve
Externí odkaz:
http://arxiv.org/abs/2206.07561
Publikováno v:
Electron. J. Combin. 30(2) (2023), #P2.7
Let $\Gamma$ be an antipodal distance-regular graph with diameter $4$ and eigenvalues $\theta_0>\theta_1>\theta_2>\theta_3>\theta_4$. Then $\Gamma$ is tight in the sense of Juri\v{s}i\'{c}, Koolen, and Terwilliger [12] whenever $\Gamma$ is locally st
Externí odkaz:
http://arxiv.org/abs/2204.07842
A Neumaier graph is a non-complete edge-regular graph containing a regular clique. A Neumaier graph that is not strongly regular is called a strictly Neumaier graph. In this work we present a new construction of strictly Neumaier graphs, and using Ja
Externí odkaz:
http://arxiv.org/abs/2109.14281
Autor:
Koolen, Jack H., Gebremichel, Brhane
In this paper we show that there does not exist a strongly regular graph with parameters $(1911,270,105,27)$.
Comment: 13 pages, 2 tables
Comment: 13 pages, 2 tables
Externí odkaz:
http://arxiv.org/abs/2109.04000