Báo cáo toán học: "Tight Upper Bounds for the Domination Numbers of Graphs with Given Order and Minimum Degree, II " pdf
Báo cáo toán học: "Tight Upper Bounds for the Domination Numbers of Graphs with Given Order and Minimum Degree, II." pdf
... graph of order n with domination number at least 3 and minimum degree δ satisfyingn −2√n −4 ≤ δ ≤ n −√2√n.Tight Upper Bounds for the Domination Numbers of Graphs with Given Order and Minimum ... combinatorics 7 (2000), #R58 19[2] W. Edwin Clark and Larry A. Dunning, Tight Upper Bounds for the Domination Numbers of Graphs with Given Order and Minimum Degree, Electron. J. Combin.4 (1997), no. ... in the case of δ3(n). For thisit is useful to find circulant graphs of order n with large minimum degree and with domination number at least 3. This turns out to be related to the existence of...
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Báo cáo toán học: "TIGHT UPPER BOUNDS FOR THE DOMINATION NUMBERS OF GRAPHS WITH GIVEN ORDER AND MINIMUM DEGREE" pdf
... γ(n, δ). We establish these values inSections 2, 3 and 4.TIGHT UPPER BOUNDS FOR THE DOMINATION NUMBERS OF GRAPHS WITH GIVEN ORDER AND MINIMUM DEGREEW. Edwin ClarkUniversity of South FloridaTampa, ... y.IfA⊆V then we let A denote the subgraph of G induced by A.Table 1 contains the value of γ(n, δ) for n ≤ 16, 0 ≤ δ ≤ n − 1 if the value isknown, otherwise upper and lower bounds for γ(n, ... to be the 8-cycle with 4 diameters added, and G10= G4∪ G6. This leaves only G9 and G11. See appendix B for these graphs, namely the graphs listed there as G(9 3 3) and G(11 3 4) the...
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Báo cáo toán học: "A new bound on the domination number of graphs with minimum degree two" docx
... is of interest to determine upper bounds on the domination number of a graph. In 1989, McCuaig and Shepherd [12]presented the beautiful result that the domination number of a connected graph with minimum ... supremum of γ(G)/|V (G)| over 2-connected cubic graphs is at least 9/2 6.Molloy and Reed [1 3] showed that the domination number of a random cubic graph of order n lies between 0.236 n and 0.3126n with ... L¨owenstein and D. Rautenbach, Domination in graphs with minimum degree atleast two a nd large girth. Graphs Combin. 24 (2008), 37–46.[12] W. McCuaig and B. Shepherd, Domination in graphs with minimum...
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Báo cáo toán học: "New Upper Bounds for the Size of Permutation Codes via Linear Programmin" pdf
... application of Theorem is 9 µ(6, 5, 5) 34. For this reason, the upper bounds do not contribute to any improvement of the results given by Theorem 7 for the range of values considered in Tables 1 and ... provides the values of the coefficients ai, considered asreal variables. On the other hand, if there exists an (n, d)− permutatio n code C whosesize reaches the upper bound a∗then the the numbers ... and d. In [15], H. Tarnanen uses the conjugacy scheme of the group Snin order to obtain new upper bounds fo r the size of a permutation code. We use this method toobtain new upper bounds for...
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Báo cáo toán học: "Improved Upper Bounds for the Laplacian Spectral Radius of a Graph" docx
... lemmas and some new and sharp upper bounds for λ(G), which are better than all of the above mentioned upper bounds in some sense, and determine the extremal g r aphs which achieve these upper bounds. ... (14) is the best in all known upper bounds for G2, and bound (18) is the best in all known upper bounds for G3. Finally,bound (22) is the best upper bound for G1 and bound (1 8) is the second-best ... characterized by the degree and the average 2-degree of the vertices. As a matter of fact, we can also utilize othercharacteristics of the vertex to estimate the Laplacian spectral radius of graphs. The definition...
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Báo cáo toán học: " Tight performance bounds for two-way opportunistic amplify-and-forward wireless relaying networks with TDBC protocols" ppt
... 2 and 3 are the comparison of the ergodiccapacity versus K. Due to the lower bounds of both PDF and CDF employed, the ergodic capacity is t he upper bound.FromFigure2,itisobservedthatwhenthedirect ... Figures 4 and 5, we investigate the effect of pathloss exponent on the system performance. In the simu-lation, only the symmetric c hannels are considered and the values of ω1k and ω2kare ... statistical descriptions of the end-to-end SNRs for the systems without direct linkshould be given with simple close d-form expressions.However, observing the results given in [16,17], we findthat...
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Báo cáo toán học: "Improved Upper Bounds for Self-Avoiding Walks in Zd" ppt
... approximations of the roots for specific values of d are found easily, and so are the inverses of the roots of smallest modulus giving us the entries of first line of table 2. the electronic journal of combinatorics ... denotes the identitymatrix and A is the state transfer matrix of the automaton. Consequently, the root of smallest modulus of the denominator polynomial of the generatingfunction is given by the ... of the limited memory k, all of these walks will behaveexactly the same in the future, and thus it is sufficient to identify the state with its representative and to keep track of the number of...
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Báo cáo toán học: "Constructive Upper Bounds for Cycle-Saturated Graphs of Minimum Size" doc
... may force the number of spokes to be a multiple of four, and thus the number of vertices not in the hub is a multiple of 4k, and thus the graph justdescribed has n − k ≡ 0mod4k vertices on the ... number of vertices from the hub. the electronic journal of combinatorics 13 (2006), #R29 4Constructive Upper Bounds for Cycle-Saturated Graphs of Minimum SizeRonald GouldDepartment of Mathematics ... count the number of edges in F (n, l). First, there are l + 1 edges on the cycle Cl+1.Thenumber of edges in the clique and those joining the clique and the cycle totall−22− 1. The matching...
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Báo cáo toán học: "NEW UPPER BOUNDS ON THE ORDER OF CAGES1" pps
... simple. The upper bound on the girth of graphs CD(n, q), together with the statement in Theorem 2.1 regardingdiameter of cages, implies that for every k ≥ 3 there exists a family of graphs of large ... provide upper bounds on the orders of (k, g)-cages.Namely,Theorem 2.1 [7] Let G be a k-regular graph of girth at least g having the leastnumber of vertices. Then the girth of G is g and the diameter ... constructed by F¨uredi, Seress and the authors,see [9]. The fact that the orders of these constructions actually meet the upper bound in (2) for q odd follows from [13]. Therefore the constructions we...
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Báo cáo toán học: "Conjectured Combinatorial Models for the Hilbert Series of Generalized Diagonal Harmonics Modules" docx
... summation formula for their generatingfunction and giving bijective proofs of the equivalence of different pairs of statistics.As before, these bijections imply that all the new statistics have the ... illustrated by the two preceding examples, where the leftmost positionis valid in one case and invalid in the other.)This lemma, together with the discussion preceding it, completes the proof of formula(18). ... Vh,k(n) is the submodule of DHnconsisting of zero and those polynomials f thatare homogeneous of degree h in the x-variables and homogeneous of degree k in the y-variables.We can now form the Frobenius...
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