Báo cáo toán học: "On the Theory of Pfaffian Orientations" pot
Báo cáo toán học: "On the Theory of Pfaffian Orientations" pot
... equals the sign of the permutation i
1
j
1
i
n
j
n
of
12 (2n).
Each nonzero term of the expansion of the Pfaffian of A(D) equals x(P ) or −x(P )
where P is a perfect matching of G.Ifs(D, P) denote the ... all
the vertices belong to the base B
0
, and the embedding of each edge uses at most one
bridge. The set of the edges embedded entirely on the base wi...
Báo cáo toán học: "On the Theory Of Pfaffian Orientations. II. T -joins, k-Cuts, and Duality of Enumeration" potx
... G
s
=(V
s
,E
s
)
the graph obtained from G by odd splitting of all vertices of T and even splitting of
all vertices of V − T. If the edge f
of G
s
is the image of the edge f of G then we let
x
s
f
= ... one-to-one correspondence with the
perfect matchings P
W
of G
s
. Note that P
W
contains the set of the images of the
edges of W . This together with...
Báo cáo toán học: "On the Energy of Unitary Cayley Graphs" pot
... completes the proof of the theorem.
In the next theorem we show that the degree of hyperenergeticity grows at least
exponentially with t he number of distinct prime divisors of n by making use of the ... m.
3. If α(λ) is the multiplicity of the eigenvalue λ of X
n
, then λα(λ) is a multiple of
φ(n).
3. ENERGY OF UNITARY CAYLEY GRAPHS
We first give a direct pro...
Báo cáo toán học: " On the boundedness of the solutions in nonlinear discrete Volterra difference equations" pot
... α(j) = 0, 0 ≤ j ≤ n. Then the solution of (4.4) and (4.5) is bounded
if and only if the condition (5.5) is satisfied.
Proof. The proof is immediate consequence from proof of Theorem 4.3 with Remark ... condition for the
boundedness of all solutions of (1.1) and the scalar case of (1.1), respectively.
The next result provides a sufficient condition for the boundedness of...
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