相关论文: Cameron-Liebler sets in Hamming graphs
Cameron-Liebler sets of subspaces in projective spaces were studied recently by Blokhuis, De Boeck and D'haeseleer (Des. Codes Cryptogr., 2019). In this paper, we discuss Cameron-Liebler sets in bilinear forms graphs, obtain several…
We survey results for Cameron-Liebler sets and low degree Boolean functions for Hamming graphs, Johnson graphs and Grassmann graphs from the point of view of association schemes. This survey covers selected results in finite geometry,…
Cameron-Liebler sets of k-spaces were introduced recently by Y. Filmus and F. Ihringer. We list several equivalent definitions for these Cameron-Liebler sets, by making a generalization of known results about Cameron-Liebler line sets in…
Cameron-Liebler line classes and Cameron-Liebler k-classes in PG(2k+1,q) are currently receiving a lot of attention. Links with the Erd\H{o}s-Ko-Rado results in finite projective spaces occurred. We introduce here in this article the…
Cameron-Liebler sets were originally defined as collections of lines (`line classes') in $\mathrm{PG}(3,q)$ sharing certain properties with line classes of symmetric tactical decompositions. While there are many equivalent…
Consider a group $G$ acting on a set $\Omega$, the vector $v_{a,b}$ is a vector with the entries indexed by the elements of $G$, and the $g$-entry is 1 if $g$ maps $a$ to $b$, and zero otherwise. A $(G,\Omega)$-Cameron-Liebler set is a…
In this article, we study degree one Cameron-Liebler sets of generators in all finite classical polar spaces, which is a particular type of a Cameron-Liebler set of generators in this polar space, [9]. These degree one Cameron-Liebler sets…
We investigate Cameron-Liebler sets of planes in the Klein quadric $Q^+(5,q)$ in PG$(5,q)$. We prove that there are many examples of such Cameron-Liebler sets of planes in the Klein quadric. More specifically, we provide an incomplete list…
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…
We study Cayley graphs of abelian groups from the perspective of quantum symmetries. We develop a general strategy for determining the quantum automorphism groups of such graphs. Applying this procedure, we find the quantum symmetries of…
In this paper we investigate graph inverse semigroups which are subsemigroups of compact-like topological semigroups. More precisely, we characterise graph inverse semigroups which admit a compact semigroup topology and describe graph…
We characterize the set of planar locally finite Cayley graphs, and give a finite representation of these graphs by a special kind of finite state automata called labeling schemes. As a result, we are able to enumerate and describe all…
In this paper we consider bi-Cohen-Macaulay graphs, and give a complete classification of such graphs in the case they are bipartite or chordal. General bi-Cohen-Macaulay graphs are classified up to separation. The inseparable…
In this article we start a systematic study of the bi-Lipschitz geometry of lamplighter graphs. We prove that lamplighter graphs over trees bi-Lipschitzly embed into Hamming cubes with distortion at most~$6$. It follows that lamplighter…
The set of semialgebraic graphs having countable list-chromatic numbers is characterized. Some other related sets of graphs having countable list-chromatic numbers also are.
We compute numerically the homology of several graph complexes in low loop orders, extending previous results.
In this short note we formulate a stabilizer formalism in the language of noncommutative graphs. The classes of noncommutative graphs we consider are obtained via unitary representations of compact groups, and suitably chosen operators on…
In this article we complete the work of enumerating typical abelian coverings of Cayley graphs, by reducing the problem to enumerating certain subgroups of finite abelian groups.
We classify the finite connected-homogeneous digraphs, as well as the infinite such digraphs with precisely one end. This completes the classification of all the locally finite connected-homogeneous digraphs.
In this paper, we study representations of Hom-Lie algebroids, give some properties of Hom-Lie algebroids and discuss equivalent statements of Hom-Lie algebroids. Then, we prove that two known definitions of Hom-Lie algebroids can be…