Báo cáo toán học: "The excessive [3]-index of all graphs" ppsx

... cycles. Let ¯ d be the average degree of vertices of G.Then α(G) ≥  n ¯ d/2. Proof. Since G contains no 3 or 5 cycles, we have α(G) ≥ d 1 (v) (consider the neighbors of v)andα(G) ≥ 1+d 2 (v) (consider ... 2 − ( k−1 k ) n k−1 k d 1 k . Proof. Immediate from Theorem 3. This improves Denley’s Theorem 4. References 1. Denley, T., The Independence number of graphs with large odd girth, Th...

Ngày tải lên: 07/08/2014, 06:20

... to the set of arcs of a base circle, such that adjacent vertices of G are mapped to intersecting arcs. The width (in a representation) of a point P of the base circle is the number of representing ... .Thewidth of  is the maximum width of the points of the base circle. (This is not the maximum number of pairwise intersecting arcs.) The arc-width of a g raph G is the min...

Ngày tải lên: 07/08/2014, 06:22

... following proofs. Let G be a graph and let v be a vertex of G . The neighborhood of v in G is denoted by N(v), i.e. N(v) = {w : wv ∈ E(G)}. Denote by ∆(G) the maximum degree of all vertices of a graph ... d(v 2 ), , d(v n )) denotes the diagonal matrix of vertex degrees of G, and d(v) denotes the degree of the vertex v of G. The Laplacian spectrum of G can be denoted by SL...

Ngày tải lên: 07/08/2014, 21:21

... (V C ,C)ofG(V,E). The set C of all cycles forms a subspace of (E, ⊕, ·) which is called the cycle space of G.AbasisBof the cycle space C is called a cycle basis of G(V, E) [2]. The dimension of the ... minimal cycle basis of G. The remainder G ∗ of G after all cycles C β , β ∈ K are removed by the above procedure is composed of Y ∗ and those edges of H that are not conta...

Ngày tải lên: 07/08/2014, 06:22

... positive integer and let G be a graph. A set M of matchings of G, all of which of size m, is called an [m]-covering of G if  M∈M M = E(G). G is called [m]-coverable if it has an [m]-covering. ... is minimum is called an excessive [m]-factorization of G and the number of match ings it contains is a graph parameter called excessive [m]-index and denoted by χ ′ [m] (G) (the...

Ngày tải lên: 08/08/2014, 01:20

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Ngày tải lên: 05/08/2014, 10:20

Ngày tải lên: 05/08/2014, 10:20

Ngày tải lên: 05/08/2014, 10:20

... set P (S) of all right translations) of the semigroup S forms a semigroup under the composition of mappings. By the translational hull of S, we mean a subsemigroup Ω(S) consisting of all bitranslations ... a(bρ) for all a, b ∈ S. A left translation λ and a right translation ρ of S are said to be linked if a(λb)=(aρ)b for all a, b ∈ S. In this case, we call the pair (λ, ρ)...

Ngày tải lên: 06/08/2014, 05:20