Displaying similar documents to “The Laplacian spectrum of some digraphs obtained from the wheel”

Sharp Upper Bounds on the Signless Laplacian Spectral Radius of Strongly Connected Digraphs

Weige Xi, Ligong Wang (2016)

Discussiones Mathematicae Graph Theory

Similarity:

Let G = (V (G),E(G)) be a simple strongly connected digraph and q(G) be the signless Laplacian spectral radius of G. For any vertex vi ∈ V (G), let d+i denote the outdegree of vi, m+i denote the average 2-outdegree of vi, and N+i denote the set of out-neighbors of vi. In this paper, we prove that: (1) (1) q(G) = d+1 +d+2 , (d+1 ≠ d+2) if and only if G is a star digraph [...] ,where d+1, d+2 are the maximum and the second maximum outdegree, respectively [...] is the digraph on n vertices...

Limit points of eigenvalues of (di)graphs

Fu Ji Zhang, Zhibo Chen (2006)

Czechoslovak Mathematical Journal

Similarity:

The study on limit points of eigenvalues of undirected graphs was initiated by A. J. Hoffman in 1972. Now we extend the study to digraphs. We prove: 1. Every real number is a limit point of eigenvalues of graphs. Every complex number is a limit point of eigenvalues of digraphs. 2. For a digraph D , the set of limit points of eigenvalues of iterated subdivision digraphs of D is the unit circle in the complex plane if and only if D has a directed cycle. 3. Every limit point of eigenvalues...

Cancellation of direct products of digraphs

Richard H. Hammack, Katherine E. Toman (2010)

Discussiones Mathematicae Graph Theory

Similarity:

We investigate expressions of form A×C ≅ B×C involving direct products of digraphs. Lovász gave exact conditions on C for which it necessarily follows that A ≅ B. We are here concerned with a different aspect of cancellation. We describe exact conditions on A for which it necessarily follows that A ≅ B. In the process, we do the following: Given an arbitrary digraph A and a digraph C that admits a homomorphism onto an arc, we classify all digraphs B for which A×C ≅ B×C.

On graphs all of whose {C₃,T₃}-free arc colorations are kernel-perfect

Hortensia Galeana-Sánchez, José de Jesús García-Ruvalcaba (2001)

Discussiones Mathematicae Graph Theory

Similarity:

A digraph D is called a kernel-perfect digraph or KP-digraph when every induced subdigraph of D has a kernel. We call the digraph D an m-coloured digraph if the arcs of D are coloured with m distinct colours. A path P is monochromatic in D if all of its arcs are coloured alike in D. The closure of D, denoted by ζ(D), is the m-coloured digraph defined as follows: V( ζ(D)) = V(D), and A( ζ(D)) = ∪_{i} {(u,v) with colour i: there exists a monochromatic...