نتایج جستجو برای: g regular

تعداد نتایج: 555121  

2007
Daniel Gagliardi Michael L. Gargano Louis V. Quintas

A regular graph G is called vertex transitive if the automorphism group of G contains a single orbit. In this paper we define and consider another class of regular graphs called neighborhood regular graphs abbreviated NR. In particular, let G be a graph and N [v] be the closed neighborhood of a vertex v of G. Denote by G(N [v]) the subgraph of G induced by N [v]. We call G NR if G(N [v]) ∼= G(N...

2006
Vladimir Nikiforov

Suppose a graph G have n vertices, m edges, and t triangles. Letting λn (G) be the largest eigenvalue of the Laplacian of G and μn (G) be the smallest eigenvalue of its adjacency matrix, we prove that λn (G) ≥ 2m2 − 3nt m (n2 − 2m) , μn (G) ≤ 3n3t− 4m3 nm (n2 − 2m) , with equality if and only if G is a regular complete multipartite graph. Moreover, if G is Kr+1-free, then λn (G) ≥ 2mn (r − 1) (...

Journal: :Symmetry 2012
Egon Schulte Jörg M. Wills

Combinatorially regular polyhedra are polyhedral realizations (embeddings) in Euclidean 3-space E of regular maps on (orientable) closed compact surfaces. They are close analogues of the Platonic solids. A surface of genus g > 2 admits only finitely many regular maps, and generally only a small number of them can be realized as polyhedra with convex faces. When the genus g is small, meaning tha...

Journal: :IJAC 1996
Walter D. Neumann Lawrence Reeves

In [ECHLPT] and [S] it is shown that if the fundamental group of a Seifert fibred 3manifold is not virtually nilpotent then it has an automatic structure. In the unpublished 1992 preprint [G2] Gersten constructs a biautomatic structure on the fundamental group of any circle bundle over a hyperbolic surface. He asks if the same can be done for the above Seifert fibered 3-manifold. We show the ex...

Journal: :Discrete Mathematics 2006
Miguel Angel Fiol Ernest Garriga

In this note we study some properties of the spectrum of a connected graph G with four different eigenvalues, and (spectrally maximum) diameter three. When G is regular, this is the case, for instance, when G is a distance-regular graph. © 2006 Elsevier B.V. All rights reserved.

Journal: :Journal of Graph Theory 1995
David A. Pike

The main result of this paper completely settles Bermond's conjecture for bipartite graphs of odd degree by proving that if G is a bipartite (2k+1)-regular graph that is Hamilton decomposable, then the line graph, L(G), of G is also Hamilton decomposable. A similar result is obtained for 5-regular graphs, thus providing further evidence to support Bermond's conjecture.

Journal: :journal of sciences, islamic republic of iran 2011
g.h. esslamzadeh

in this article we study two different generalizations of von neumann regularity, namely strong topological regularity and weak regularity, in the banach algebra context. we show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. then we consider strong topological regularity of certain concrete algebras. moreover we obtain ...

2010
A. A. MAKHNEV V. V. NOSOV

A strongly regular graph with λ = 0 and μ = 3 is of degree 3 or 21. The automorphisms of prime order and the subgraphs of their fixed points are described for a strongly regular graph Γ with parameters (162, 21, 0, 3). In particular, the inequality |G/O(G)| ≤ 2 holds true for G = Aut(Γ).

Journal: :Discrete Applied Mathematics 2009
Weigen Yan Yeong-Nan Yeh

Let G be a simple graph and let S(G) be the subdivision graph of G, which is obtained from G by replacing each edge of G by a path of length two. In this paper, by the Principle of Inclusion and Exclusion we express the matching polynomial and Hosoya index of S(G) in terms of the matchings of G. Particularly, if G is a regular graph or a semi-regular bipartite graph, then the closed formulae of...

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