Spectra of transformation digraphs of a regular digraph

2010 ◽  
Vol 58 (5) ◽  
pp. 555-561 ◽  
Author(s):  
Juan Liu ◽  
Jixiang Meng
Keyword(s):  
Regular Digraph

scholarly journals Constructions for arc-transitive digraphs

1995 ◽  
Vol 59 (1) ◽  
pp. 61-80 ◽  
Author(s):  
Marston Conder ◽  
Peter Lorimer ◽  
Cheryl Praeger
Keyword(s):  
Positive Integer ◽  
Permutation Group ◽  
Finite Groups ◽  
Transitive Permutation Group ◽  
Group Of Automorphisms ◽  
Representations Of Finite Groups ◽  
Regular Digraph

AbstractA number of constructions are given for arc-transitive digraphs, based on modifications of permutation representations of finite groups. In particular, it is shown that for every positive integer s and for any transitive permutation group p of degree k, there are infinitely many examples of a finite k-regular digraph with a group of automorphisms acting transitively on s-arcs (but not on (s + 1)-arcs), such that the stabilizer of a vertex induces the action of P on the out-neighbour set.

The Regular Digraph Associated to a Poset

2017 ◽  
Vol 42 (3) ◽  
pp. 995-1009
Author(s):  
M. Afkhami ◽  
S. Bahrami ◽  
K. Khashyarmanesh
Keyword(s):  
Regular Digraph

Hamilton Cycles in Random Regular Digraphs

1994 ◽  
Vol 3 (1) ◽  
pp. 39-49 ◽  
Author(s):  
Colin Cooper ◽  
Alan Frieze ◽  
Michael Molloy
Keyword(s):  
Hamilton Cycles ◽  
Regular Digraph

We prove that almost every r-regular digraph is Hamiltonian for all fixed r ≥ 3.

On the Aα-spectrum of joined union of digraphs

2021 ◽  
pp. 2150086
Author(s):  
Hilal A. Ganie
Keyword(s):  
Adjacency Matrix ◽  
Laplacian Matrix ◽  
Diagonal Matrix ◽  
Signless Laplacian Matrix ◽  
Signless Laplacian ◽  
Adjacency Matrices ◽  
Matrix Formula ◽  
Regular Digraph

Let [Formula: see text] be a digraph of order [Formula: see text] and let [Formula: see text] be the adjacency matrix of [Formula: see text] Let Deg[Formula: see text] be the diagonal matrix of vertex out-degrees of [Formula: see text] For any real [Formula: see text] the generalized adjacency matrix [Formula: see text] of the digraph [Formula: see text] is defined as [Formula: see text] This matrix generalizes the spectral theories of the adjacency matrix and the signless Laplacian matrix of [Formula: see text]. In this paper, we find [Formula: see text]-spectrum of the joined union of digraphs in terms of spectrum of adjacency matrices of its components and the eigenvalues of an auxiliary matrix determined by the joined union. We determine the [Formula: see text]-spectrum of join of two regular digraphs and the join of a regular digraph with the union of two regular digraphs of distinct degrees. As applications, we obtain the [Formula: see text]-spectrum of various families of unsymmetric digraphs.

scholarly journals ON THE REGULAR DIGRAPH OF IDEALS OF COMMUTATIVE RINGS

2012 ◽  
Vol 88 (2) ◽  
pp. 177-189 ◽  
Author(s):  
M. AFKHAMI ◽  
M. KARIMI ◽  
K. KHASHYARMANESH
Keyword(s):  
Finite Number ◽  
Commutative Ring ◽  
Direct Product ◽  
Commutative Rings ◽  
Nonzero Divisor ◽  
Vertex Set ◽  
Regular Digraph ◽  
Finite Direct Product

AbstractLet$R$be a commutative ring. The regular digraph of ideals of$R$, denoted by$\Gamma (R)$, is a digraph whose vertex set is the set of all nontrivial ideals of$R$and, for every two distinct vertices$I$and$J$, there is an arc from$I$to$J$whenever$I$contains a nonzero divisor on$J$. In this paper, we study the connectedness of$\Gamma (R)$. We also completely characterise the diameter of this graph and determine the number of edges in$\Gamma (R)$, whenever$R$is a finite direct product of fields. Among other things, we prove that$R$has a finite number of ideals if and only if$\mathrm {N}_{\Gamma (R)}(I)$is finite, for all vertices$I$in$\Gamma (R)$, where$\mathrm {N}_{\Gamma (R)}(I)$is the set of all adjacent vertices to$I$in$\Gamma (R)$.

scholarly journals Minimum Cuts of Distance-Regular Digraphs

10.37236/6167 ◽  
2017 ◽  
Vol 24 (4) ◽  
Author(s):  
Saleh Ashkboos ◽  
Gholamreza Omidi ◽  
Fateme Shafiei ◽  
Khosro Tajbakhsh
Keyword(s):  
Coming Out ◽  
Single Vertex ◽  
Minimum Cuts ◽  
Regular Digraph

In this paper, we investigate the structure of minimum vertex and edge cuts of distance-regular digraphs. We show that each distance-regular digraph $\Gamma$, different from an undirected cycle, is super edge-connected, that is, any minimum edge cut of $\Gamma$ is the set of all edges going into (or coming out of) a single vertex. Moreover, we will show that except for undirected cycles, any distance regular-digraph $\Gamma$ with diameter $D=2$, degree $k\leq 3$ or $\lambda=0$ ($\lambda$ is the number of 2-paths from $u$ to $v$ for an edge $uv$ of $\Gamma$) is super vertex-connected, that is, any minimum vertex cut of $\Gamma$ is the set of all out-neighbors (or in-neighbors) of a single vertex in $\Gamma$. These results extend the same known results for the undirected case with quite different proofs.

scholarly journals The polynomial of a non-regular digraph

1971 ◽  
Vol 38 (2) ◽  
pp. 325-341 ◽  
Author(s):  
William Bridges
Keyword(s):  
Regular Digraph
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