Báo cáo toán học: "Integral Quartic Cayley Graphs on Abelian Groups" pdf

... = Γ 12 . Hence all of the connected, regular integral graphs up to seven vertices are Cayley graphs. In other words there are exactly 12 connected, integral Cayley graphs up to seven vertices. It ... Cayley graphs with 10 vertices.  Lemma 2.23 There are exactly three connected, integral Cayley graphs with nine vertices. Proof. We show that the graphs Γ 19 , Γ 21 and Γ 24 a...

Ngày tải lên: 08/08/2014, 14:23

... Geometrical constructions There are several constructions that produce families of cubic graphs with large girth, based on configurations of points on a projective line. The points on the line PG(1,q)(qa ... by exactly one of α and β. In the first case, the permutation αβ acts on the vertices of the component as two cycles of length l/2, so (αβ) l/2 is the identity permutation on th...

Ngày tải lên: 07/08/2014, 06:22

... partition of n, the order of L.Wecallthis (unordered) partition the cycle partition corresponding to the two rows in question. Another way to think of row cycles is in terms of the permutation which ... 1-factorisations of complete graphs which we found using a variation on our search for atomic latin squares. It turns out that our method is general enough to construct a perfect 1-factori...

Ngày tải lên: 07/08/2014, 08:22

... exactly once in every r ow and in every column. For a pandiagonal Latin square two additional conditions have to be satisfied. Every number 1, . . ., n has to appear exactly once in the main diagonal ... integral Cayley graphs. We remark that every set S in the Boolean algebra B(Γ) satisfies S = −S. For the construction of a Cayley graph Cay(Γ, S) we use only those S ∈ B(Γ) which do not c...

Ngày tải lên: 08/08/2014, 12:22

... T. Integral Cayley graphs over abelian groups. Elec- tronic J. Combinatorics 17 (2010), R81, 1–13. [11] Klotz, W., and Sander, T. Some properties of unitary Cayley gra phs. Electronic J. Co mbinatorics ... integral graphs see [3]. In [2] the numb er of integral graphs on n vertices is estimated. Known characterizations of integral graphs are restricted to certain graph classes...

Ngày tải lên: 08/08/2014, 14:23

... Fulkersonian if and only if Δ ∗ is Fulkersonian. We shall see that Fulkersonian hypergraphs can be used to study the integral closures of powers of monomial ideals. Let I be an arbitrary monomial ... N n if and only if Q(Δ) only has integral extremal points. One calls Δ a Fulkersonian hypergraph [2] (or paranormal [1]) if Q(Δ) only has integral extremal points. By the above observation and Le...

Ngày tải lên: 06/08/2014, 05:20

... Boston, 1993. [12] L. Lovasz, personal communication. [13] J. Konhauser, D. Velleman, and S. Wagon, Which Way Did the Bicycle Go?, Dolciani series, Mathematical Association of America, Washington, D.C. ... standard construction of a graph that realizes a particular group is due to Frucht, see [7]. Recall that the construction begins with one vertex for each group element. Vertices correspondi...

Ngày tải lên: 07/08/2014, 06:20

... John Wiley and Sons, 1990. [W] Written on the Wall, a list of conjectures of Graffiti. Ramseyan Properties of Graphs by Ermelinda DeLaVina delavina@math.uh.edu Siemion Fajtlowicz siemion@math.uh.edu University ... y} blue if G + {e} belongs to P ,andred - otherwise. A class, i.e., a property P of graphs will be called Ramseyan if large graphs from P contain large monochromatic subgraphs...

Ngày tải lên: 07/08/2014, 06:20

... existence of a non-trivial family of graphs which are perfect w.r.t strong orthogonality. The final section contains some concluding remarks and open problems. 2 Upper bounds In this section we prove ... in the second coloring. For a survey of the results on orthogonal edge colorings the reader is referred to [1]. The results on orthogonal edge coloring naturally translate to results on...

Ngày tải lên: 07/08/2014, 06:20

... Section 2 establishes our notation, gives a few basic definitions, and proves several lemmas that simplify the proof of Theorem 1.2, which is contained in Section 3. Section 4 contains comments on ... integer partitions. Proposition 3.5. Shriekless graphs not containing K − 5 correspond to integer par- titions which either have three or fewer parts or whose parts are all of size one. Alter...

Ngày tải lên: 07/08/2014, 06:20