Báo cáo toán học: "An Infinite Family of Graphs with the Same Ihara Zeta Function" potx

... families of pairs of graphs which share the same zeta function. 1. Introduction In 2009 , Cooper described an infinite family of non-isomorphic pairs of graphs which she conjectured had the same Ihara ... 2010 Mathematics Subject Classification: 05C38 Abstract In 2009, Cooper presented an infinite family of pairs of graphs which were con- jectured to have t...

Ngày tải lên: 08/08/2014, 12:22

... has the property that if the initial design in the infinite family has the collection of five blocks mentioned above then so do all other members of the infinite family; 3) Give a design having the ... b 8 and l 5 = b 18 . Therefore, there is an infinite family of non-embeddable 2 - (2λ +2,λ+1,λ)designs with λ =3(2 m ) − 1. The author would like to thank the De...

Ngày tải lên: 07/08/2014, 06:20

... sense than the poset of graphs ordered by the operations of edge contraction and vertex deletion. (That this poset of graphs does not contain an infinite antichain is a famous theorem of Robertson ... sequence of length three at its beginning, a long alternating permutation starting with the maximal element of the permutation and ending with the entry 7 at the...

Ngày tải lên: 07/08/2014, 06:20

... v 5 ,whichgetslabel3k−9. The result is a (9k − 26)-regular graph of order 27k − 79. Finally, we would like to know whether there are further cores of dense maximal triangle-free graphs. If not then the answer to the ... conjecture of Jin [8], saying that there are graphs of arbitrarily large chromatic number with this property. Another infinite sequence of dense triangle...

Ngày tải lên: 07/08/2014, 06:22

... a hinge of G.If|B [x,y ] |≥3, then the set of edges of G having x and y as ends, together with the edges of ˆ G of the form e 2 B ,forB ∈B 2 [x,y ] , induces a cleavage unit of G. Furthermore, ... B 1 ,B 2 , ,B r be the blocks of H containing the edges of P . There are no other blocks of H. If any B i has two or more edges, then let u, v be the attachments of...

Ngày tải lên: 07/08/2014, 08:20

... derive the order of D + f from the number of solutions of y 2 = f(x). In particular, when y 2 = f(x) is in a certain class of elliptic curves, there is an explicit formula for the order of D + f . ... D(f ρ ). The proof of the converse is similar to this. the electronic journal of combinatorics 14 (2007), #N25 5 that any element of the Galois group acts as σ(δ) =...

Ngày tải lên: 07/08/2014, 15:22

... + cr(F  ) = 1 + (k − 1) = k if the claim holds true in the base case k = 3. Hence we can finish the proof of the theorem with further Lemma 3.3 which takes care of k = 3. ✷ Lemma 3.2 Let F be ... D. Bokal, On the crossing number of Cartesian products with paths, J. of Combina- torial Theory ser. B 97 (2007), 381–384. [2] D. Bokal, Infinite families of crossing-critica...

Ngày tải lên: 07/08/2014, 21:20

... to the zones. Case 1 :TherowsofL are selected from the same zone, say the j-th zone. Referring to the proof of Theorem 1 we see that the leading columns of C i ’s form a rearrangement of the ... so the negatives of each of the patterns in the columns of matrix (1) appear among the columns of H, off the block H jj .Thusall eight patterns appear off the blo...

Ngày tải lên: 07/08/2014, 06:22

... the same property: hence the induction hypothesis for w  will imply the required result for w. Using Lemma 3, write w = uµ(y)v. Note that, from the proof of the second part of Lemma 3, the word ... 1 of Lemma 2. The existence of the decomposition for finite words is proved in [10], in the proof of Theorem 6.4. The uniqueness is proved in [11], Lemma 2.2. Finall...

Ngày tải lên: 07/08/2014, 06:22

... K 2 -factor of G into one of G  . Again we consider the weak Cartesian product G =  G where the components of the root vertex are the roots of the G . Again we let the unit fibers inherit the labelings ... where ∆ is the largest degree of G. We conclude the section with the following analogue for infinite graphs. Theorem 2.1 Let n be a cardinal number, and...

Ngày tải lên: 07/08/2014, 15:22