Zobrazeno 1 - 10
of 650
pro vyhledávání: '"P. Haemers"'
A divisible design graph is a graph whose adjacency matrix is an incidence matrix of a (group) divisible design. Divisible design graphs were introduced in 2011 as a generalization of $(v,k,\lambda)$-graphs. Here we describe four new infinite familie
Externí odkaz:
http://arxiv.org/abs/2404.09902
We provide three infinite families of graphs in the Johnson and Grassmann schemes that are not uniquely determined by their spectrum. We do so by constructing graphs that are cospectral but non-isomorphic to these graphs.
Externí odkaz:
http://arxiv.org/abs/2305.16858
Autor:
Haemers, Willem, Topcu, Hatice
We complete the determination of the signed graphs for which the adjacency matrix has all but at most two eigenvalues equal to $\pm 1$. The unsigned graphs and the disconnected, the bipartite and the complete signed graphs with this property have alr
Externí odkaz:
http://arxiv.org/abs/2301.01623
Autor:
Haemers, Willem H., Topcu, Hatice
We present the first steps towards the determination of the signed graphs for which the adjacency matrix has all but at most two eigenvalues equal to 1 or -1. Here we deal with the disconnected, the bipartite and the complete signed graphs. In additi
Externí odkaz:
http://arxiv.org/abs/2109.02522
Autor:
Gu, Xiaofeng, Haemers, Willem H.
The toughness $t(G)$ of a graph $G=(V,E)$ is defined as $t(G)=\min\{\frac{|S|}{c(G-S)}\}$, in which the minimum is taken over all $S\subset V$ such that $G-S$ is disconnected, where $c(G-S)$ denotes the number of components of $G-S$. We present two t
Externí odkaz:
http://arxiv.org/abs/2104.03845
Autor:
Haemers, Willem H.
Hoffman's ratio bound is an upper bound for the independence number of a regular graph in terms of the eigenvalues of the adjacency matrix. The bound has proved to be very useful and has been applied many times. Hoffman did not publish his result, an
Externí odkaz:
http://arxiv.org/abs/2102.05529
Autor:
Akbari, Saieed, Haemers, Willem H., Hosseinzadeh, Mohammad Ali, Kabanov, Vladislav V., Konstantinova, Elena V., Shalaginov, Leonid
Publikováno v:
Discrete Mathematics, 2021
A Deza graph $G$ with parameters $(n,k,b,a)$ is a $k$-regular graph with $n$ vertices such that any two distinct vertices have $b$ or $a$ common neighbours. The children $G_A$ and $G_B$ of a Deza graph $G$ are defined on the vertex set of $G$ such th
Externí odkaz:
http://arxiv.org/abs/2101.06877
Publikováno v:
Frontiers in Cardiovascular Medicine, Vol 10 (2024)
The autonomic nervous system plays a crucial role in atrial fibrillation pathophysiology. Parasympathetic hyperactivity result in a shortening of the action potential duration, a reduction of the conduction wavelength, and as such facilitates reentry
Externí odkaz:
https://doaj.org/article/31ff6aa9238a4628ace12dcbedfbc3fe
A conference matrix of order $n$ is an $n\times n$ matrix $C$ with diagonal entries $0$ and off-diagonal entries $\pm 1$ satisfying $CC^\top=(n-1)I$. If $C$ is symmetric, then $C$ has a symmetric spectrum $\Sigma$ (that is, $\Sigma=-\Sigma$) and eige
Externí odkaz:
http://arxiv.org/abs/2004.05829
A universal adjacency matrix of a graph $G$ with adjacency matrix $A$ is any matrix of the form $U = \alpha A + \beta I + \gamma J + \delta D$ with $\alpha \neq 0$, where $I$ is the identity matrix, $J$ is the all-ones matrix and $D$ is the diagonal
Externí odkaz:
http://arxiv.org/abs/2004.02499