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On the automorphism group of a johnson graph

WebAbstract. Using an analysis of the clique structure and only the most elementary group theory, we determine the automorphism group of the Johnson graph J ( n, i), for n ≠ 2 i. … Web1 de nov. de 2024 · Then X is a Johnson graph or is doubly covered by a Johnson graph. More precisely, in the latter case X is the quotient of the Johnson graph J (2 d, d) by an automorphism of the form τω, where τ is the automorphism sending each d-set to its complement, and ω is an element of order at most 2 in Aut (X) with at least 8 fixed …

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Web1 de jan. de 1973 · We are now able to list the automorphism groups for several common families of graphs. 20 The Automorphism Group of a Graph Chapt. 3 3-4. Thm. 3-18. Graphs with a Given Automorphism Group Every finite group is the automorphism group of some graph. For a proof of this theorem, due to Frucht [ F 4 ] , see Section 4-2. … 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 ≤ … inc p2 https://acebodyworx2020.com

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Web4 de jan. de 2016 · It isn't the Johnson graphs themselves that were a scourge to theorists. It's more that the Johnson graphs showed that certain difficult structural properties (mentioned above) are possible and nobody knew a general method for handling these properties. Once Babai showed that only the Johnson graphs caused that structure, the … 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. inc or incorporated

[1412.5055] On the automorphism group of a Johnson graph

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On the automorphism group of a johnson graph

Topics in Graph Automorphisms and Reconstruction - Cambridge …

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 Web1 de dez. de 2014 · The automorphism group of the Johnson graph $J(n,i)$ is $S_n \times T \rangle$ where $T$ is the complementation map $A \mapsto \{1,\ldots,n\} \setminus A$. …

On the automorphism group of a johnson graph

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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 ≤ 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, … 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 ...

There is a distance-transitive subgroup of isomorphic to . In fact, , except that when , . Web1 de jan. de 1973 · This chapter defines the automorphism group of a graph. The chapter introduces various binary operations on permutation groups to aid in computing …

WebDOI: 10.22108/TOC.2024.127225.1817 Corpus ID: 119705994; A note on the automorphism group of the Hamming graph @article{Mirafzal2024ANO, title={A note on the automorphism group of the Hamming graph}, author={S. Morteza Mirafzal and Meysam Ziaee}, journal={arXiv: Group Theory}, year={2024} } WebKey-words: designs, codes in graphs, Johnson graph, 2-transitive permuta-tion group, neighbour-transitive, Delandtsheer design, ag-transitive, anti ag-transitive. Mathematics Subject Classi cation (2010): 05C25, 20B25, 94B60. 1 Introduction The Johnson graphs are ubiquitous in mathematics, perhaps because of their many useful properties.

WebFormally, an automorphism of a graph G = (V, E) is a permutation σ of the vertex set V, such that the pair of vertices (u, v) form an edge if and only if the pair (σ(u), σ(v)) also …

Web27 de fev. de 2024 · The inner automorphism group of Q 8 is given by the group modulo its center, i.e. the factor group Q 8 /{e, e}, which is isomorphic to the Klein four-group V. The full automorphism group of Q 8 is isomorphic to S 4 , the symmetric group on four letters (see Matrix representations below), and the outer automorphism group of Q 8 is … in body scan body fat percentageWebA continuous-time quantum walk on a graph G is given by the unitary matrix U ( t ) = exp ( − i t A ) , where A is the adjacency matrix of G . We say G has pretty good state transfer between vertices a and b if for any ϵ > 0 , there is a time t , where the ( a , b ) -entry of U ( t ) satisfies U ( t ) a , b ≥ 1 − ϵ . This notion was introduced by Godsil (2011). inc outfitsWeb20 de nov. de 2024 · In 1938 Frucht (2) showed that every finite group is isomorphic to the group of some graph. Since then Frucht, Izbicki, and Sabidussi have considered various other properties that a graph having a given group may possess. (For pertinent references and definitions not given here see Ore (4).) inc or inclWeb1 de nov. 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 … inc outdoor livingWebAmongst the many classes of uniform subset graphs it has only been determined that Aut ( Γ ( 2 k + 1, k, 0)), the automorphism group of the so called Odd graphs, is S n, and more recently, Ramras and Donovan [ 2] proved that Aut ( … inc parentingWeb9 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 … inc ou incWebUsing an analysis of the clique structure and only the most elementary group theory, we determine the automorphism group of the Johnson graph J ( n, i), for n ≠ 2 i. Although … inc pain