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 satisfying n −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...

Ngày tải lên: 07/08/2014, 06:22

... γ(n, δ). We establish these values in Sections 2, 3 and 4. TIGHT UPPER BOUNDS FOR THE DOMINATION NUMBERS OF GRAPHS WITH GIVEN ORDER AND MINIMUM DEGREE W. Edwin Clark University of South Florida Tampa, ... 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 is known...

Ngày tải lên: 07/08/2014, 06:20

... 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...

Ngày tải lên: 08/08/2014, 12:23

... 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 a i , considered as real variables. On the other hand, if there exists an (n, d)− permutatio n code C whose size reaches...

Ngày tải lên: 08/08/2014, 12:22

... 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 G 2 , and bound (18) is the best in all known upper bounds for G 3 . Finally, bound (22) is the bes...

Ngày tải lên: 08/08/2014, 12:23

... 2 and 3 are the comparison of the ergodic capacity versus K. Due to the lower bounds of both PDF and CDF employed, the ergodic capacity is t he upper bound.FromFigure2,itisobservedthatwhenthe direct ... Figures 4 and 5, we investigate the effect of path loss exponent on the system performance. In the simu- lation, only the symmetric c hannels are considered...

Ngày tải lên: 20/06/2014, 21:20

... 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 identity matrix and A is the state transfer matrix of the automaton. Consequently, the root of smallest modulus of the...

Ngày tải lên: 07/08/2014, 06:20

... 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 just described has n − k ≡ 0mod4k vertices on the ... number of vertices from the hub. the electronic journal of combinatorics 13 (2006), #R29 4 Constructive Upper Bounds for Cycle-Saturated Graphs of Minimum...

Ngày tải lên: 07/08/2014, 13:21

... simple. The upper bound on the girth of graphs CD(n, q), together with the statement in Theorem 2.1 regarding diameter 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 least number of vert...

Ngày tải lên: 07/08/2014, 06:22

... summation formula for their generating function 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 position is valid in one case and invalid in the other.) This lemma, together with the discussion prec...

Ngày tải lên: 07/08/2014, 08:20