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

Báo cáo toán học: "THE INDEPENDENCE NUMBER OF DENSE GRAPHS WITH LARGE ODD GIRTH" ppsx

... cycles. Let¯d be the average degree of vertices of G.Thenα(G) ≥n¯d/2.Proof. Since G contains no 3 or 5 cycles, we have α(G) ≥ d1(v) (consider the neighbors of v)andα(G) ≥ 1+d2(v) (consider ... 2−(k−1k)nk−1kd1k.Proof. Immediate from Theorem 3.This improves Denley’s Theorem 4.References1. Denley, T., The Independence number of graphs with large odd girth, The Electronic Journal of Combinatorics ... graphs of larger odd girth.Lemma 2: Let G have odd girth 2k + 1 or greater (k ≥ 2). Thenα(G) ≥v∈G12(1 + d1(v)+···+ dk−1(v))1+d1(v)+···+ dk(v).Proof. Randomly label the vertices of...

3
324
0

Báo cáo toán học: "The arc-width of a graph" ppsx

... to the set of arcs of a base circle, such that adjacent vertices of G aremapped to intersecting arcs. The width (in a representation) of a point P of thebase circle is the number of representing ... .Thewidth of  is themaximum 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 minimal possiblewidth of such ... minors of theclass aw(G) ≤ k. Such a list is similar to the one we get for path-width. ByLemma 8 some of the elements of the two parallel lists are the same. It is knownthat the number of excluded...

8
299
0

Báo cáo toán học: "The Laplacian Spread of Tricyclic Graphs" ppt

... followingproofs. Let G be a graph and let v be a vertex of G . The neighborhood of v in G isdenoted by N(v), i.e. N(v) = {w : wv ∈ E(G)}. Denote by ∆(G) the maximum degree of all vertices of a graph ... d(v2), , d(vn)) denotesthe 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 bySL(G) = (µ1(G), µ2(G), ... maximumLaplacian spread among all tricyclic gr aphs of order n ≥ 11. Moreover, fo r 5 ≤ n ≤ 10,if G is one with maximum Laplacian spread of all tricyclic gra phs of order n, then G isnecessary...

18
246
0

Báo cáo toán học: "Minimal Cycle Bases of Outerplanar Graphs" ppsx

... (VC,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 cyclebasis of G(V, E) [2]. The dimension of the ... minimal cycle basis of G. The remainder G∗ of G after all cyclesCβ, β ∈ K are removed by the above procedure is composed of Y∗and those edges of H that are not contained in any of the cycles ... cycle basis is chordless if all its cycles are chordless.The length |C| of a cycle C is the number of its edges. The length (B) of a cyclebasis B is sum of the lengths of its cycles: (B)=C∈B|C|.Aminimal...

14
359
0

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

... 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∈MM = E(G). G iscalled [m]-coverable if it has an [m]-covering. ... isminimum is called an excessive [m]-factorization of G and the number of match ingsit contains is a graph parameter called excessive [m]-index and denoted by χ′[m](G)(the value of χ′[m](G) ... (and the search for a directproof of Theorem 1 remains an open challenge!). We shall actually prove a strongerresult, namely Theorem 2 below, for the proof of which we need a case-by-case analysis.Before...

17
312
0

Báo cáo toán học: "The Ext groups of the C*-algebras associated with irrational rotations " pptx

...

4
318
0

Báo cáo toán học: "The linear span of projections in simple C*-algebras " pot

...

8
324
0

Báo cáo toán học: "The spectral flavour of Scott Brown''''s techniques " pot

...

11
267
0

Báo cáo toán học: "The invariant subspaces of a Volterra operator " pot

...

11
388
0

Báo cáo toán học: " The Translational Hull of a Strongly Right or Left Adequate Semigroup" pdf

... set P (S) of all right translations) of the semigroupS forms a semigroup under the composition of mappings. By the translationalhull of S, we mean a subsemigroup Ω(S) consisting of all bitranslations ... a(bρ) for all a, b ∈ S. A left translation λ anda 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) a bitranslation of S.ThesetΛ(S) ... S.ThesetΛ(S) of all left∗This research is supported by the National Natural Science Foundation of China (Grant No.10671151); the NSF grant of Shaanxi Province, grant No. 2004A10 and the SF grant of...

7
347
0