Báo cáo toán học: "Commuting Involution Graphs for 3-Dimensional Unitary Group" docx

... Commuting Involution Graphs for 3-Dimensional Unitary Groups Alistaire Everett School of Mathematics The University of Manchester Oxford Road, Manchester, M13 9PL, UK a.everett@maths.manchester.ac.uk Submitted: ... X are involutions, then C(G, X) is called a commuting involution graph. This paper studies C(G, X) when G is a 3-dimensional projective special unitary group and X...

Ngày tải lên: 08/08/2014, 14:23

... graph for H ( √ m) . Then any circuit in G(∞, (u/n) √ m) is of the form v 1 → S(v 1 ) → S 2 (v 1 ) → S 3 (v 1 ) → · · · → S k−1 (v 1 ) → v 1 for a unique elliptic mapping S ∈ H ( √ m) and for some ... circuit in the graph G(∞, u/n) for N (Γ 0 (m)). Since n > 1, by Theorem3.1, C ∗ is of the form v → T (v) → T 2 (v) → T 3 (v) → · ·· → T k−1 (v) → v for some v ∈ ˆ Q and for a uniq...

Ngày tải lên: 08/08/2014, 01:20

Ngày tải lên: 05/08/2014, 10:20

... component of G − v is a K δ . Proof: To show f(v) ≥ 1+δ,firstnotethatitistrivialforδ = 2. Suppose the result is true for graphs with δ = k and let G have δ = k +1. Letv be a vertex of G and note that ... article is to characterize all such extremal graphs. For a graph G with n vertices we define f(G) to be the number of vertices in a longest path of G, and for a vertex v of G we define...

Ngày tải lên: 07/08/2014, 06:20

... L n . Therefore by induction π = π 0 π n−2 π n−1 with π j ∈ R L j for all 0 ≤ j ≤ n − 1. For example, let π =[3, 5, −4, 2, −1], then π 3 = a 3 a 2 a 1 ; ππ −1 3 =[−4, 3, 2, −1, 5], there- fore π 2 = ... 3.1 and 3.3]. For a proof of the general case, see for example [2, Ch. 3.3]. the electronic journal of combinatorics 11 (2004), #R83 3 From this formulation one sees immediately that...

Ngày tải lên: 07/08/2014, 08:22

... of the natural lines of investigation for Laplacian integral graphs is to focus on graphs for which the maximum degree is not very large. It is straightforward to see that if G is a connected ... conclusion is straightforward to determine. Since tr(D 4 ) =  n i=1 d 4 i and tr(A 2 D 2 ) =  n i=1 d 3 i , it suffices to find tr(ADAD) and tr(A 4 ). For the former expression, note that f...

Ngày tải lên: 07/08/2014, 21:20

... = 0. Therefore µ i − µ ′ i = 0 for all i, and so the matrices A and A ′ have the same characteristic polynomials. Thus the graphs G and G ′ are cospectral. 4 The m-equivalence of graphs 4.1. ... similarity may exist even fo r non-isomorphic graphs. In any o f these cases the graphs are called equivalent (Definition 3.3). For example any two strongly regular graphs with the same p...

Ngày tải lên: 08/08/2014, 01:20

... Ramanujan Type Congruences for a Partition Function Haijian Zhao and Zheyuan Zhong Center for Combinatorics, LPMC-TJKLC Nankai University, Tianjin, P.R. China haijian.nankai@gmail.com, ... was also proven by Baruah and Ojah [1] using the 3-dissections for ϕ(−q) −1 and ψ(q) −1 , and by Cao [4] applying the 3-dissection for (q; q) ∞ (q 2 ; q 2 ) ∞ . We will give another proof ba sed ......

Ngày tải lên: 08/08/2014, 14:22

... 26, 1996 Abstract A method for constructing cubic graphs with girths in the range 13 to 16 is described. The method is used to construct the smallest known cubic graphs for girths 14, 15 and 16. Introduction We ... [2]. AFinalNote For a given n and t, it is fairly easy to do an exhaustive search through all graphs of this type discussed above. So we were able to verify that these...

Ngày tải lên: 07/08/2014, 06:20

... exhibit for each n ≥ 4an(n, 3)-graph G n which is 3-regular if n is even and almost regular if n is odd such that γ(G n )=3n/8. We first note that it suffices to find the graphs G n for 4 ≤ n ≤ 11: For ... 3.2. (1) γ(n, n − 1) = γ r (n, n − 1)= 1for any n ≥ 1. (2) γ(n, n − 2) = γ r (n, n − 2)= 1for odd n ≥ 2. (3) γ(n, n − 2) = γ r (n, n − 2)= 2for even n ≥ 2. Proof. For each of the...

Ngày tải lên: 07/08/2014, 06:20