On the asymptotic enumeration of Cayley graphs
نویسندگان
چکیده
Abstract In this paper, we are interested in the asymptotic enumeration of Cayley graphs. It has previously been shown that almost every digraph smallest possible automorphism group: is, it is a digraphical regular representation (DRR). approach corresponding question for undirected The situation complicated by fact there two infinite families groups do not admit any graphical (GRR). strategy digraphs involved analysing separately cases where group R nontrivial proper normal subgroup N with property fixes each -coset setwise, and does not. deal graphs case such subgroup.
منابع مشابه
Asymptotic aspects of Cayley graphs
Arising from complete Cayley graphs Γn of odd cyclic groups Zn, an asymptotic approach is presented on connected labeled graphs whose vertices are labeled via equallymulticolored copies of K4 in Γn with adjacency of any two such vertices whenever they are represented by copies of K4 in Γn sharing two equally-multicolored triangles. In fact, these connected labeled graphs are shown to form a fam...
متن کاملOn the distance eigenvalues of Cayley graphs
In this paper, we determine the distance matrix and its characteristic polynomial of a Cayley graph over a group G in terms of irreducible representations of G. We give exact formulas for n-prisms, hexagonal torus network and cubic Cayley graphs over abelian groups. We construct an innite family of distance integral Cayley graphs. Also we prove that a nite abelian group G admits a connected...
متن کاملOn the eigenvalues of Cayley graphs on generalized dihedral groups
Let $Gamma$ be a graph with adjacency eigenvalues $lambda_1leqlambda_2leqldotsleqlambda_n$. Then the energy of $Gamma$, a concept defined in 1978 by Gutman, is defined as $mathcal{E}(G)=sum_{i=1}^n|lambda_i|$. Also the Estrada index of $Gamma$, which is defined in 2000 by Ernesto Estrada, is defined as $EE(Gamma)=sum_{i=1}^ne^{lambda_i}$. In this paper, we compute the eigen...
متن کاملOn the eigenvalues of normal edge-transitive Cayley graphs
A graph $Gamma$ is said to be vertex-transitive or edge- transitive if the automorphism group of $Gamma$ acts transitively on $V(Gamma)$ or $E(Gamma)$, respectively. Let $Gamma=Cay(G,S)$ be a Cayley graph on $G$ relative to $S$. Then, $Gamma$ is said to be normal edge-transitive, if $N_{Aut(Gamma)}(G)$ acts transitively on edges. In this paper, the eigenvalues of normal edge-tra...
متن کاملAsymptotic enumeration of sparse 2-connected graphs
We determine an asymptotic formula for the number of labelled 2-connected (simple) graphs on n vertices and m edges, provided that m−n→∞ and m = O(n logn) as n→∞. This is the entire range of m not covered by previous results. The proof involves determining properties of the core and kernel of random graphs with minimum degree at least 2. The case of 2-edge-connectedness is treated similarly. We...
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: Annali di Matematica Pura ed Applicata
سال: 2021
ISSN: ['1618-1891', '0373-3114']
DOI: https://doi.org/10.1007/s10231-021-01163-w