Báo cáo toán học: "Cospectral graphs on 12 vertices" potx

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Ngày tải lên: 05/08/2014, 15:20

... type of Shcherbina on the relation between pluriporlarity of graphs and holomorphicity of complex-valued functions defined on a domain in C n . In particular we establish the relation between the ... of graphs and holomorphicity of complex-valued functions. In particular, we investigate the relation between the pluripolarity of graphs and th...

Ngày tải lên: 06/08/2014, 05:20

... any nonhamiltonian Burkard–Hammer graph is contained in a maximal nonhamil- tonian Burkard–Hammer graph. So knowledge about maximal nonhamiltonian Burkard–Hammer graphs provides us certain information about nonhamiltonian Burkard–Hammer ... assume that all con- sidered in this paper maximal nonhamiltonian Burkard–Hammer graphs G = S(I ∪ K, E)haveδ(G)=|I|−k where |I|≥k...

Ngày tải lên: 06/08/2014, 05:20

... A Note on Sparse Random Graphs and Cover Graphs ∗ Tom Bohman † Alan Frieze ‡ Mikl´os Ruszinko Đ Lubos Thoma ả Department of Mathematical Sciences Carnegie Mellon University Pittsburgh, ... a constant κ<2/3, then it outputs a cover graph whp. Note that the output graph will have whp girth equal to 4. On a related note we point to [8] which surveys constructions of no...

Ngày tải lên: 07/08/2014, 06:20

... harmonic functions on certain graded graphs: the Young lattice and its generalizations. Such functions first emerged in harmonic analysis on the infinite symmetric group. Our method relies on multi- variate ... this section, we deal with an abstract graph G satisfying certain conditions listed below. In the next sections, concrete examples of G will be considered. Our assumptions...

Ngày tải lên: 07/08/2014, 06:20

... even larger Cayley graphs based on groups which A note on constructing large Cayley graphs of given degree and diameter by voltage assignments ∗ Ljiljana Brankovi´c, Mirka Miller Department of ... degree/ diameter problem,whichis to determine the largest order of a graph with given degree and diameter. Many currently known largest graphs of...

Ngày tải lên: 07/08/2014, 06:22

... irregular graphs, Graphs and Combinatorics 18 (2002), 53–57. [2] N. Biggs, Algebraic Graph Theory, Cambridge University Press, Cambridge, second edition, 1993. [3] J.A. Bondy, M. Simonovits, Cycles ... vine on P ∗ and P ∗ is the unique uv-geodesic. Proof. Suppose, for a contradiction, that H is not a vine on P ∗ .Letx ≺ v be a vertex of P ∗ at a maximum distance from u on P ∗ such th...

Ngày tải lên: 07/08/2014, 08:22

... mind, we define a partial f- factor of a graph G = (V, E) to be an ˜ f- factor of G where ˜ f( v) = f( v) ∪ {0} for all v ∈ V , and a partial f- factor of G is non-trivial if it is non-empty. Our next result ... sufficient condition for the existence of an f- factor of G. No necessary and sufficient condition for an f- factor exists when we allow |f( v)| ≥ 2, even when |f( v)|...

Ngày tải lên: 07/08/2014, 15:22

... assumptions of the lemma, hence, by induction, there is an element a j = 0 such that a j−1 + a j+1  3, a contradiction. Therefore, we may assume every second element of s is positive and every second ... (a t+1 , . . . , a k ) complies with the assumptions of the lemma (and is not a forbidden one), hence we again obtain a contradiction by induction. the electronic journal of combinatorics 15...

Ngày tải lên: 07/08/2014, 15:22

... of combinatorics 15 (2008), #N10 8 A note on the component structure in random intersection graphs with tunable clustering Andreas N. Lager˚as ∗ Mathematical Sciences and Centre for Theoretical ... in random intersection graphs. The Electronic Journal of Combinatorics, 14, #R17, 2007. [3] M. Deijfen and W. Kets. Random intersection graphs with tunable...

Ngày tải lên: 07/08/2014, 15:23

... Classification: 0 5A1 5 Abstract For a certain graph obtained by adding extra vertices and edges to the triangular lattice graph, Propp conjectured that the number of perfect matchin gs of such a graph ... consider the set of all perfect matchings of G n . Define a relation R on this set as follows: two perfect matchings have the relation R if and only if they have...

Ngày tải lên: 07/08/2014, 21:21

... graphs on 12 vertices, and report statistics related to the number of cospectral graphs. 1 Introduction Let the spectrum of a graph be the spectrum of its 0-1 adjacency matrix. In connec- tion ... isomorphism problem, it is of interest what fraction of all graphs is uniquely determined by its spectrum. Haemers conjectures that the fraction of graphs on n vertices with a cospectr...

Ngày tải lên: 07/08/2014, 21:21

... Cayley graphs on the symmetric group generated by initial reversals have unit spectral gap Filippo Cesi Dipartimento di Fisica Universit`a ... symmetric group corresponding to the Young subgroup S n2 ì S 2 and generated by initial reversals. In particular they find that the first nonzero eigenvalue, or spectral gap, of the Laplacian is always ... (2.3)...

Ngày tải lên: 07/08/2014, 21:21

... graphs without short cycles, Colloq. Math. Soc. Janos Bolyai 60 (1991) 727–732. the electronic journal of combinatorics 16 (2009), #N30 3 A note on packing graphs without cycles of length up to ... (xσ ′ (v))(yσ ′ (w))σ ′ is a packing of G. Thus we get a contradiction. Assume now that G ′ − U is a star (with at least one edge). Note that since G has no cycle...

Ngày tải lên: 07/08/2014, 21:21

... u l−s to u i along the outer cycle is a shortest path between u 0 and u i , as desired.  In what follows, we give the proof of the main theorem. Proof of Theorem 2: By Proposition 4, there exists ... 1, the generalized Petersen graph GP (n, k) is not strongly distance-balanced (strongly distance-balanced graph was introduced by K utnar et al. in [2]). In this note, we pr...

Ngày tải lên: 07/08/2014, 21:21