A design is called quasi-symmetric if it has only two block intersection numbers.
Using a method based on orbit matrices, we classify quasi-symmetric \(2\)-\((28,12,11)\)
designs with intersection ...numbers \(4\), \(6\), and an automorphism of order \(5\). There
are exactly \(31\,696\) such designs up to isomorphism.
In this paper we give a complete classification of all n-dimensional non-Lie Malcev algebras with (n−4)-dimensional annihilator over an algebraically closed field of characteristic 0. We also show ...that such algebras are special.
If $L$ is a lattice, the automorphism group of $L$ is denoted $\mathrm{Aut}(L)$. It is known that given a finite abstract group $H$, there exists a finite distributive lattice $D$ such that ...$\mathrm{Aut}(D) \cong H$. It is also known that one cannot expect to find a finite orthocomplemented distributive (Boolean) lattice $B$ such that $\mathrm{Aut}(B) \cong H$. In this paper it is shown that there does exist a finite orthomodular lattice $L$ such that $\mathrm{Aut}(L) \cong H$.
A new strongly regular graph with parameters (81,30,9,12) is found as a graph invariant under certain subgroup of the full automorphism group of the previously known strongly regular graph discovered ...in 1981 by J. H. van Lint and A. Schrijver.
Given a finite abstract group G, whenever n is sufficiently large there exist graphs with n vertices and automorphism group isomorphic to G. Let e(G, n) denote the minimum number of edges possible in ...such a graph. It is shown that for each G there always exists a graph M such that for n sufficiently large, e(G, n) is attained by adding to M a standard maximal component asymmetric forest. A characterization of the graph M is given, a formula for e(G, n) is obtained (for large n), and the minimum edge problem is re-examined in the light of these results.
The automorphisms of 2-token graphs Zhang, Ju; Zhou, Jin-Xin; Li, Yan-Tao ...
Applied mathematics and computation,
06/2023, Letnik:
446
Journal Article
Recenzirano
Let Λ=(V(Λ),E(Λ)) be a graph. The 2-token graphF2(Λ) of Λ is with vertex set all the 2-subsets of V(Λ), a pair of 2-subsets are adjacent if the symmetric difference is exactly in E(Λ). In this paper, ...it is proved that Z2n−1⋊Aut(Λ)≲Aut(F2(Λ)), where Λ is a Cartesian product of n prime graphs. Then it is shown that the equality may happen by proving that Aut(F2(Qn))≅Z2n−1⋊Aut(Qn), where Qn is the n-dimensional hypercube with n≥3. This also provides some partial answers to 25, Problem 1.3.
The Graph Extension Theorem Shult, Erhest
Proceedings of the American Mathematical Society,
01/1972, Letnik:
33, Številka:
2
Journal Article
Recenzirano
Odprti dostop
A sufficient condition is given that a transitive permutation group $G$ admits a transitive extension $G^\ast$. The condition is graph-theoretic and does not involve any direct algebraic properties ...of the group being extended. The result accounts for a fairly wide class of doubly transitive groups, including the two doubly transitive representations of the groups $\operatorname{Sp}(2n, 2)$, and the doubly transitive representations of the Higman-Sims group, and the Conway group (.3).
The paper is devoted to classify nilpotent Jordan algebras of dimension up to five over an algebraically closed field F of characteristic not 2. We obtained a list of 35 isolated non-isomorphic ...5-dimensional nilpotent non-associative Jordan algebras and 6 families of non-isomorphic 5-dimensional nilpotent non-associative Jordan algebras depending either on one or two parameters over an algebraically closed field of characteristic ≠2,3. In addition to these algebras we obtained two non-isomorphic 5-dimensional nilpotent non-associative Jordan algebras over an algebraically closed field of characteristic 3.
We characterise the primitive 2-closed groups G of rank at most four that are not the automorphism group of a graph or digraph and show that if the degree is at least 2402 then there are just two ...infinite families or G⩽AΓL1(pd), the 1-dimensional affine semilinear group. These are the first known examples of non-regular 2-closed groups that are not the automorphism group of a graph or digraph.
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