Báo cáo toán học: "Distinguishing numbers for graphs and groups" docx

... |Γ|≤m! and the subset {y 1 , ,y j } satisfies 1. φ(y i )=i for each i, 2. y i+1 is in Γ i−1 .y i for each i from 2 to j − 1, and y 1 is in Γ j−1 .y j , then j ≤ m and |Γ i−1 .y i |≥j − i + 2for each ... shows this and two other graphs with the same automorphism group and demonstrates that all three have different distinguishing numbers. This example disproves a conjecture in [...

Ngày tải lên: 07/08/2014, 08:20

... vertices. This implies that the only graphs which have fix(G) = n−1 are the complete graphs and the empty graphs. On the other hand, the graphs with fix(G) = 0 are the rigid graphs [1], which have trivial ... are adjacent if and only if there exists some index i such that u j = v j for all j < i, u i = v i , and u j = v i and v j = u i for all j > i. Lemma 15. The...

Ngày tải lên: 07/08/2014, 21:21

... > 1 for all v ∈ V (T ) \ {u} and deg(v) ≤ 2 ℵ 0 for all v ∈ V (T ). For each α ∈ A, we define a distinguishing {0, 1}-labeling l − α such that u and all neighbors of u in T are labeled 0, and ... 2 ℵ 0 , and R has the following property: (∗) For any finite disjoint subsets X and Y of V (R), there are infinitely many vertices z of R such that zx ∈ E(R) for all x ∈ X and z...

Ngày tải lên: 07/08/2014, 15:22

... of as S 1 k−1 . We will find exact values for sat(n, S 2 r+1 ) for all r and establish upper and lower bounds for sat(n, S t r+1 ) for t ≥ 3. Theorem 14. For n ≥ 10, sat(n, S 2 4 ) = ⌈ 9n 10 ⌉. Proo ... T ∗ k and S 4 and it is easy to see in this case the conclusion holds. For k = 5, there exist only three trees none of which is T k -saturated for any tree on 5 vertices e...

Ngày tải lên: 08/08/2014, 01:20

... harmonic functions. We give also a Guelfond and Polya type theorem in the case of harmonic function. 2. Notations and Results For all z = re iθ ∈ C and n ∈ N we put: e 1 (z) ≡ 1,e n (z)=  r k cos ... Ma y 24, 2004 Abstract. For harmonic and separately harmonic functions, we give results similar to the Carlson-Boas theorem. We give also harmonic analogous of the Polya and Guelfo...

Ngày tải lên: 06/08/2014, 05:20

... possibilities for future research in this area. Computing β(G) for other classes of greedoids, e.g., rooted graphs, rooted digraphs, trees, posets (both the single and double shelling antimatroids) and ... Convexity and Related Combinatorial Geometry, (D. C. Kay and M. Breen, eds.), Marcel Dekker, Inc., New York (1982). [21] E. McMahon, On the greedoid polynomial for rooted gr...

Ngày tải lên: 07/08/2014, 06:20

... with highest weight ρ for type C n . Substituting x i = e ε i /2 for i =1, 2, ,n in the weight labelings for both Aztec diamond graphs gives (P )(Q)=Ch(Ψ ρ ). Theorem 6 Let P and Q be Aztec diamonds ... basis for Ψ ρ . In a similar fashion, we show that perfect matchings on pairs of Aztec diamond graphs can be used to index a basis for Ψ ρ for the classical Lie algebras of...

Ngày tải lên: 07/08/2014, 08:20

... results for d = 2, k = 1, β 0 = 1, β 1 = 2, while item (ii) results for d = 2, k = 1, β 0 = 2, β 1 = 1. Moreover, upon setting k = 0 and β 0 = d + 1 in Theorem 2.2, we obta in Formula (1.2) (and ... colouring mentioned above. The resulting statistics for Catalan numbers (and the obvious generalization to Fuß–Catalan numbers obtained by replacing winding numbers with the corre...

Ngày tải lên: 08/08/2014, 14:23

... (3) and (4) we conclude | det(X reg n )| = a creg n , which proves the theorem. Proof of Theorem 3: We assume that the rows and columns of X n are ordered such that the regular characters and ... on regular classes and the singular character table X sing n is defined analogously. Let a creg n =  µ class regular a µ ,b creg n =  µ class regular b µ and define a csing n and b csing...

Ngày tải lên: 07/08/2014, 07:21

... and R ≥ 0 T1.1:  R T a  b F R =    {{a − 2 | 1} | 0} if R = 0 and b = 1 (a − 1)(b − 1 + R) if b is even and (R, b) = (0, 0) (a − 1)(b − 1 + R)∗ if b is odd and (R, b) = (0, 1) T1.2: For ... positions where for each of the permutation of i of  and j of F, we insert a variable (symbolic) number of T in-between the  and F. For example, A11 is all positions with one ...

Ngày tải lên: 08/08/2014, 14:22