On the automorphism group of a johnson graph

Author: tuyb

August undefined, 2024

Web1 de abr. de 2005 · The merged Johnson graph J (n, m)I is the union of the distance i graphs J (n, m)i of the Johnson graph J (n, m) for i ∈ I, where Ø ≠ I ⊆ {1,..., m } and 2 ≤ … Web8 de fev. de 2024 · [1702.02568v3] The automorphism groups of Johnson graphs: revisited The Johnson graph $J(n, m)$ is defined as the graph whose vertex set is the set of all $m$-element subsets of $\{1, . . ., n \}$, and two vertices are adjacent whenever the cardinality of their... Accessible arXiv

The Automorphism Group of a Johnson Graph - ResearchGate

Web13 de nov. de 2024 · In this paper, we study a class of regular graphs, which is related to the Grassmann graph. This class of graphs is called the doubled Grassman graph. The … WebThe automorphism group of G is equal to the automorphism group of the complement G. WHY? Note that automorphisms preserve not only adjacency, but non-adjacency as well. Hence, φ∈ Aut(G) if and only if φ∈ Aut(G). It follows that Aut(G) = Aut(G). Robert A.Beeler,Ph.D. (EastTennesseeStateUniversity)Graph Automorphism Groups … the lot edmonton food trucks

Automorphisms and regular embeddings of merged Johnson graphs

Webgroup of permutations is generated by (xi,xj), (yk,yℓ), and (x,y) Qn i=1(xi,yi). Thus, the automorphism group is isomorphic to S2 n ⋉Z2. The Petersen Graph is one of the most important graphs. In fact, en-tire books have been written about the Petersen graph [16]. The Petersen graph K(5,2) is the graph where the vertex set is all 2-element ... Web23 de dez. de 2024 · Babai conjectured that Hamming and Johnson graphs are the only primitive distance-regular graphs of diameter whose automorphism group has sublinear minimal degree. We confirm this conjecture for non-geometric primitive distance-regular graphs of bounded diameter. Web1 de jan. de 2024 · PDF The Johnson graph $J(n, m)$ is defined as the graph whose vertex set is the set of all $m$-element subsets of $\\{1, . . . , n \\}$, and two... Find, read and ... tick tock biscuits

A characterization of Johnson and Hamming graphs and proof of …

On the automorphism group of a johnson graph

Automorphism Group of Graphs (Supplemental Material for Intro to Graph ...

Web20 de out. de 2024 · For a simple graph G = ( V, E) we let Γ V ( G) define the group of automorpisms over the set of vertices V that preserve G 's edge structure. Similarly, we define Γ E ( G) to be the group of … WebWhile it is easy to characterize the graphs on which a given transitive permutation groupG acts, it is very difficult to characterize the graphsX with Aut (X)=G. We prove here that for the certain transitive permutation groups a simple necessary condition is also sufficient. As a corollary we find that, whenG is ap-group with no homomorphism ontoZ p wrZ p , almost …

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Web1 de nov. de 2024 · As an application, we confirm Babai's conjecture on the minimal degree of the automorphism group of distance-regular graphs of bounded diameter. This … Web10 de abr. de 2024 · Keywords: subdivision graph, line graph, connectivity, automorphism group, Hamil-tonian graph. AMS Sub ject classiﬁcation: 05C25, 05C38,05C75. Constructing new families of graphs from families ...

Web9 de dez. de 2014 · In Ramras and Donovan [\emph{SIAM J. Discrete Math}, 25(1): 267-270, 2011], it is conjectured that if $n=2i$, then the automorphism group of the Johnson … Webadjacent, whereas c(v,w) = a0,whenv,ware not adjacent, then G is a stablegraph, that is, the automorphism group of the bipartite double cover of G is isomorphic with the group Aut(G)×Z2. Finally, we show that the Johnson graph J(n,k)is a stable graph. Keywords. Automorphism group; bipartite double cover of a graph; Grassmann graph; stable ...

Web1 de jul. de 2024 · An asymmetric coloring of a graph is a coloring of its vertices that is not preserved by any non-identity automorphism of the graph. The motion of a graph is the minimal degree of its automorphism group, i.e., the minimum number of elements that are moved (not fixed) by any non-identity automorphism. We confirm Tom Tucker's “Infinite … Web1 de abr. de 2005 · The merged Johnson graph J (n,m)I is the union of the distance i graphs J (n,m)i of the Johnson graph J (n,m) for i∈I, where ∅≠I⊆ {1,…,m} and 2≤m≤n/2. We find the automorphism groups ...

Web1 de jul. de 2024 · Abstract. We prove that a distance-regular graph with a dominant distance is a spectral expander. The key ingredient of the proof is a new inequality on the …

WebAn automorphism of a graph is a graph isomorphism with itself, i.e., a mapping from the vertices of the given graph G back to vertices of G such that the resulting graph is isomorphic with G. The set of automorphisms … tick tock body curlsWeb1 de dez. de 2014 · Using an analysis of the clique structure and only the most elementary group theory, this work determines the automorphism group of the Johnson graph J (n,i) for $n\neq2i$ for the case of n=2i. 12 Highly Influential View 5 excerpts, references background and methods Automorphisms and regular embeddings of merged Johnson … the lot farmers marketWeb1 de abr. de 2005 · The merged Johnson graph J(n, m) I is the union of the distance i graphs J(n, m) i of the Johnson graph J(n, m) for i ∈ I, where Ø ≠ I ⊆ {1,...,m} and 2 ≤ m ≤ n/2. We find the automorphism groups of these graphs, and deduce that their only regular embedding in an orientable surface is the octahedral map on the sphere for J(4, 2) 1, … tick tock bluetooth alarm clock stereo