Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
On the Characteristic Polynomial of $n$-Cayley Digraphs
View through CrossRef
A digraph $\Gamma$ is called $n$-Cayley digraph over a group $G$, if there exists a semiregular subgroup $R_G$ of Aut$(\Gamma)$ isomorphic to $G$ with $n$ orbits. In this paper, we represent the adjacency matrix of $\Gamma$ as a diagonal block matrix in terms of irreducible representations of $G$ and determine its characteristic polynomial. As corollaries of this result we find: the spectrum of semi-Cayley graphs over abelian groups, a relation between the characteristic polynomial of an $n$-Cayley graph and its complement, and the spectrum of Calye graphs over groups with cyclic subgroups. Finally we determine the eigenspace of $n$-Cayley digraphs and their main eigenvalues.
The Electronic Journal of Combinatorics
Title: On the Characteristic Polynomial of $n$-Cayley Digraphs
Description:
A digraph $\Gamma$ is called $n$-Cayley digraph over a group $G$, if there exists a semiregular subgroup $R_G$ of Aut$(\Gamma)$ isomorphic to $G$ with $n$ orbits.
In this paper, we represent the adjacency matrix of $\Gamma$ as a diagonal block matrix in terms of irreducible representations of $G$ and determine its characteristic polynomial.
As corollaries of this result we find: the spectrum of semi-Cayley graphs over abelian groups, a relation between the characteristic polynomial of an $n$-Cayley graph and its complement, and the spectrum of Calye graphs over groups with cyclic subgroups.
Finally we determine the eigenspace of $n$-Cayley digraphs and their main eigenvalues.
Related Results
On isomorphisms of m-Cayley digraphs
On isomorphisms of m-Cayley digraphs
The isomorphism problem for digraphs is a fundamental problem in graph theory. This problem for Cayley digraphs has been extensively investigated over the last half a century. In t...
The Cayley Isomorphism Property for Cayley Maps
The Cayley Isomorphism Property for Cayley Maps
The Cayley Isomorphism property for combinatorial objects was introduced by L. Babai in 1977. Since then it has been intensively studied for binary relational structures: graphs, d...
Domination of Polynomial with Application
Domination of Polynomial with Application
In this paper, .We .initiate the study of domination. polynomial , consider G=(V,E) be a simple, finite, and directed graph without. isolated. vertex .We present a study of the Ira...
Finite edge-transitive Cayley graphs and rotary Cayley maps
Finite edge-transitive Cayley graphs and rotary Cayley maps
This paper aims to develop a theory for studying Cayley graphs, especially for those with a high degree of symmetry. The theory consists of analysing several types of basic Cayley ...
Power Cayley Graphs of Dihedral Groups with Certain Order
Power Cayley Graphs of Dihedral Groups with Certain Order
Combination of the concepts of power graph and Cayley graph associated to groups has led to the introduction to two new variations of Cayley graph known as the union power Cayley g...
On the Cayley Isomorphism Problem for Cayley Objects of Nilpotent Groups of Some Orders
On the Cayley Isomorphism Problem for Cayley Objects of Nilpotent Groups of Some Orders
We give a necessary condition to reduce the Cayley isomorphism problem for Cayley objects of a nilpotent or abelian group $G$ whose order satisfies certain arithmetic properties to...
Sub-exponential Time Parameterized Algorithms for Graph Layout Problems on Digraphs with Bounded Independence Number
Sub-exponential Time Parameterized Algorithms for Graph Layout Problems on Digraphs with Bounded Independence Number
AbstractFradkin and Seymour (J Comb Theory Ser B 110:19–46, 2015) defined the class of digraphs of bounded independence number as a generalization of the class of tournaments. They...