1. Transitive regular q-analogs of graphsDean Crnković, Vedrana Mikulić Crnković, Andrea Švob, Matea Zubović Žutolija, 2025, original scientific article Abstract: In 1976, Delsarte introduced the notion of q-analogs of designs, and q-analogs of graphs were introduced recently by M. Braun et al. In this paper, we extend that study by giving a method for constructing transitive regular q-analogs of graphs. Further, we illustrate the method by giving some examples. Additionally, we introduced the notion of q-analogs of quasi-strongly regular graphs and give examples of transitive q-analogs of quasi-strongly regular graphs coming from spreads.
Keywords: q-ary design, q-ary graph, regular graph, transitive group
Published in RUP: 03.11.2025; Views: 267; Downloads: 1
 Full text (382,29 KB) |
2. Bounding s for vertex-primitive s-arc-transitive digraphs of alternating and symmetric groupsJunyan Chen, Lei Chen, Michael Giudici, Jing Jian Li, Cheryl E. Praeger, Binzhou Xia, 2025, original scientific article Abstract: Determining an upper bound on s for finite vertex-primitive s-arc-transitive digraphs has received considerable attention dating back to a question of Praeger in 1990. It was shown by Giudici and Xia that the smallest upper bound on s is attained for some digraph admitting an almost simple s-arc-transitive group. In this paper, based on the work of Pan, Wu and Yin, we prove that s<=2 in the case where the group is an alternating or symmetric group.
Keywords: digraph, vertex-primitive, s-arc-transitive, alternating group, symmetric group
Published in RUP: 22.10.2025; Views: 328; Downloads: 1
Full text (397,42 KB) |
3. Edge-transitive core-free Nest graphsIstván Kovács, 2025, original scientific article Abstract: A finite simple graph Γ is called a Nest graph if it is regular of valency 6 and admits an automorphism ρ with two orbits of the same length such that at least one of the subgraphs induced by these orbits is a cycle. We say that Γ is core-free if no non-trivial subgroup of the group generated by ρ is normal in Aut(Γ). In this paper, we show that, if Γ is edge-transitive and core-free, then it is isomorphic to one of the following graphs: the complement of the Petersen graph, the Hamming graph H(2,4), the Shrikhande graph and a certain normal 2-cover of K_{3,3} by ℤ_2^4.
Keywords: bicirculant, edge-transitive, primitive permutation group
Published in RUP: 10.09.2025; Views: 418; Downloads: 3
Full text (466,20 KB) |
4. |
5. |
6. Linking rings structures and semisymmetric graphs : combinatorial constructionsPrimož Potočnik, Steve Wilson, 2018, original scientific article Keywords: graphs, automorphism group, symmetry, locally arc-transitive graphs, symmetric graphs, cycle structure, linking ring structure
Published in RUP: 03.01.2022; Views: 2493; Downloads: 19
Full text (397,55 KB) |
7. The automorphism groups of non-edge transitive rose window graphsEdward Tauscher Dobson, István Kovács, Štefko Miklavič, 2015, original scientific article Abstract: In this paper, we determine the full automorphism groups of rose window graphs that are not edge-transitive. As the full automorphism groups of edge-transitive rose window graphs have been determined, this complete the problem of calculating the full automorphism group of rose window graphs. As a corollary, we determine which rose window graphs are vertex-transitive. Finally, we determine the isomorphism classes of non-edge-transitive rose window graphs.
Keywords: rose window graphs, automorphism group, isomorphism problem, vertex-transitive graph
Published in RUP: 31.12.2021; Views: 2677; Downloads: 44
Full text (275,74 KB) |
8. |
9. |
10. |
