Báo cáo toán hoc:"Which Cayley graphs are integral" docx
Báo cáo toán hoc:"Which Cayley graphs are integral" docx
... integral Cayley graphs and
introduce some infinite family of connected integ r al Cayley graphs.
The main results are the following.
Theorem 1.1 There are exactly seven connected cubic integral Cayley ... C
m
and D
2n
are used for the cyclic group of order m and dihedral gro up
of order 2n (n > 2).
The main question that we are concerned here is the following:
Which Cayle...
Báo cáo toán học: "Random Cayley graphs are expanders: a simple proof of the Alon–Roichman theorem" potx
... theorem of N. Alon and Y. Roichman [4] asserts that random Cayley graphs are
expanders. Specifically, they study the spectrum of the Cayley graphs obtained by selecting k
elements, independently and ... is a family of graphs {G
i
| i>0}, where G
i
is a (n
i
,d,)-
expander, and d are constants independent of n
i
,andthen
i
tend to infinity in i. Graphs
with these properties...
Báo cáo toán học: "Almost all graphs with 2.522n edges are not 3-colorable" ppt
... V. Chv´atal, Almost all graphs with 1.44n edges are 3-colorable, Random Structures &
Algorithms, 2 (1991), 11–28.
[5] P. Erd˝os, A. R´enyi, On the evolution of random graphs, Publication of ... for non-k-colorability are
given for k>3.
1991 Mathematics Subject Classification: Primary 05C80; Secondary 05C15.
1 Introduction
Let N(n, m, A) denote the number of graphs with vertices...
Báo cáo toán học: "Explicit Ramsey graphs and orthonormal labelings" pdf
... and describe an explicit construction of triangle free graphs with
independence numbers m and Ω(m
3/2
) vertices. Our graphs are Cayley graphs and their construc-
tion is based on some of the ... easy; see [14]) that the independence number of G does not exceed θ(G). The
graphs G
n
we construct here are triangle free graphs on n vertices satisfying θ(G
n
)=Θ(n
2/3
), and
hence...
Báo cáo toán học: "Counting two-graphs related to trees" ppt
... reduced two -graphs, and let E(F) denote the
class of two -graphs containing no member of F as a substructure. If f
n
and g
n
denote the
numbers of labelled n-element two -graphs and reduced two -graphs ... Y unchanged.) When I speak of the pentagon and hexagon two -graphs below, I
mean the two -graphs obtained from the pentagon and hexagon graphs by this procedure.
All this material c...
Báo cáo toán học: "On Extremal Graphs With No Long Paths" docx
... non-hamiltonian graphs which barely miss satisfying Dirac’s condition.
We are sure this must be known, but we have not found it in the literature. We
are grateful to Arthur Hobbs [6], who made us aware of ... every
component of G − v. ✷
Summarizing, we now know all extremal graphs, G with f (G)=2δ +1. The
connected extremal graphs are those given in Theorem 3 along with the trivial...
Báo cáo toán học: "Recognizing circulant graphs of prime order in polynomial time" doc
... particular, circulant graphs have been studied intensively in
the literature. These graphs are easily seen to be vertex transitive. In the case of a
prime vertex number n circulant graphs are known to ... only vertex transitive
graphs. Because of their high symmetry, Cayley graphs are ideal models for commu-
nication networks. Routing and weight balancing is easily done on su...
Báo cáo toán học: "Recognizing circulant graphs in polynomial time: An application of association schemes" pot
... full
cycle.
Cayley graphs, and in particular circulants, have been studied intensively in the lit-
erature. These graphs are vertex-transitive. In the case of a prime vertex number n,
circulants are ... on the choice of the pair (x, y) ∈ γ.
The elements of Γ are called basic relations, their graphs basic graphs, and the numbers
p
γ
α,β
are called the structure constants of the...
Báo cáo toán học: "Holes in graphs" potx
... up G(k, t) was to obtain graphs with more vertices than n
1
and
still having -holes in large subgraphs. Next we consider a random “contraction” of G(k, t)
to obtain graphs with fewer than n
1
vertices ... M. Capalbo, Y. Kohayakawa, V. R¨odl, A. Ruci´nski, E. Szemer´edi, Near-
optimum universal graphs for graphs with bounded degrees, APPROX-RANDOM
2001, LNCS 3139 (2001) 170-180
the el...
Báo cáo toán học: "On the Graphs of Hoffman-Singleton and Higman-Sims" docx
... properties is sharp (hence the
parentheses).
Together with the 2 Hoffman-Singleton subgraphs H
1
and H
2
, Lemma 35 produces
252 Hoffman-Singleton subgraphs. A further 252 of them are obtained by applying ... subgraphs.
The next two Lemmas show that there are no further Hoffman-Singleton subgraphs: the
total number of 5-cycles in G is 443 520 (Lemma 41), each contained in two Hoffman-
Singlet...
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