Eigenvalues of the derangement graph
نویسندگان
چکیده
منابع مشابه
Eigenvalues of the derangement graph
We consider the Cayley graph on the symmetric group Sn generated by derangements. It is well known that the eigenvalues of this graph are indexed by partitions of n. We investigate how these eigenvalues are determined by the shape of their corresponding partitions. In particular, we show that the sign of an eigenvalue is the parity of the number of cells below the first row of the corresponding...
متن کاملOn the Spectrum of the Derangement Graph
We derive several interesting formulae for the eigenvalues of the derangement graph and use them to settle affirmatively a conjecture of Ku regarding the least eigenvalue.
متن کاملAutomorphism Group of the Derangement Graph
In this paper, we prove that the full automorphism group of the derangement graph Γn (n ≥ 3) is equal to (R(Sn) ⋊ Inn(Sn)) ⋊ Z2, where R(Sn) and Inn(Sn) are the right regular representation and the inner automorphism group of Sn respectively, and Z2 = 〈φ〉 with the mapping φ : σ φ = σ−1, ∀σ ∈ Sn. Moreover, all orbits on the edge set of Γn (n ≥ 3) are determined.
متن کاملThe Main Eigenvalues of the Undirected Power Graph of a Group
The undirected power graph of a finite group $G$, $P(G)$, is a graph with the group elements of $G$ as vertices and two vertices are adjacent if and only if one of them is a power of the other. Let $A$ be an adjacency matrix of $P(G)$. An eigenvalue $lambda$ of $A$ is a main eigenvalue if the eigenspace $epsilon(lambda)$ has an eigenvector $X$ such that $X^{t}jjneq 0$, where $jj$ is the all-one...
متن کاملEigenvalues of the Cayley Graph of Some Groups with respect to a Normal Subset
Set X = { M11, M12, M22, M23, M24, Zn, T4n, SD8n, Sz(q), G2(q), V8n}, where M11, M12, M22, M23, M24 are Mathieu groups and Zn, T4n, SD8n, Sz(q), G2(q) and V8n denote the cyclic, dicyclic, semi-dihedral, Suzuki, Ree and a group of order 8n presented by V8n = < a, b | a^{2n} = b^{4} = e, aba = b^{-1}, ab^{...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2010
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2009.10.002