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In this paper, we study the order of a maximal clique in an amply regular graph with a fixed smallest eigenvalue by considering a vertex that is adjacent to some (but not all) vertices of the maximal clique. As a consequence, we show that if a strongly regular graph contains a Delsarte clique, then the parameter $mu$ is either small or large. Furthermore, we obtain a cubic polynomial that assures that a maximal clique in an amply regular graph is either small or large (under certain assumptions). Combining this cubic polynomial with the claw-bound, we rule out an infinite family of feasible parameters $(v,k,lambda,mu)$ for strongly regular graphs. Lastly, we provide tables of parameters $(v,k,lambda,mu)$ for nonexistent strongly regular graphs with smallest eigenvalue $-4, -5, -6$ or $-7$.
In this paper we show that if $theta$ is a $T$-design of an association scheme $(Omega, mathcal{R})$, and the Krein parameters $q_{i,j}^h$ vanish for some $h in T$ and all $i, j in T$, then $theta$ consists of precisely half of the vertices of $(Omeg
In analogy with the Singleton defect for classical codes, we propose a definition of rank defect for Delsarte rank-metric codes. We characterize codes whose rank defect and dual rank defect are both zero, and prove that the rank distribution of such
For a non-negative integer $sle |V(G)|-3$, a graph $G$ is $s$-Hamiltonian if the removal of any $kle s$ vertices results in a Hamiltonian graph. Given a connected simple graph $G$ that is not isomorphic to a path, a cycle, or a $K_{1,3}$, let $delta(
Let $G_{m,n,k} = mathbb{Z}_m ltimes_k mathbb{Z}_n$ be the split metacyclic group, where $k$ is a unit modulo $n$. We derive an upper bound for the diameter of $G_{m,n,k}$ using an arithmetic parameter called the textit{weight}, which depends on $n$,
We study the accuracy of triangulation in multi-camera systems with respect to the number of cameras. We show that, under certain conditions, the optimal achievable reconstruction error decays quadratically as more cameras are added to the system. Fu