... 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...
... 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...
... 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...
... 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...
... 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...
... 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...
... 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...
... 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...
... 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...
... 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...