منابع مشابه
Energy of Graphs, Matroids and Fibonacci Numbers
The energy E(G) of a graph G is the sum of the absolute values of the eigenvalues of G. In this article we consider the problem whether generalized Fibonacci constants $varphi_n$ $(ngeq 2)$ can be the energy of graphs. We show that $varphi_n$ cannot be the energy of graphs. Also we prove that all natural powers of $varphi_{2n}$ cannot be the energy of a matroid.
متن کاملPrefab posets' Whitney numbers
We introduce a natural partial order ≤ in structurally natural finite subsets the cobweb prefabs sets recently constructed by the present author. Whitney numbers of the second kind of the corresponding subposet which constitute Stirling-like numbers' triangular array-are then calculated and the explicit formula for them is provided. Next-in the second construction-we endow the set sums of prefa...
متن کاملTranslated Whitney and r-Whitney Numbers: A Combinatorial Approach
Using a combinatorial approach, we introduce the translated Whitney numbers. This seems to be more natural than to write a product of anarithmetical progression in terms of a power variable and conversely. We also extend our ideas to translated r-Whitney numbers of both kinds and to translated Whitney-Lah numbers.
متن کاملThe Tutte Dichromate and Whitney Homology of Matroids
We consider a specialization YM (q, t) of the Tutte polynomial of a matroid M which is inspired by analogy with the Potts model from statistical mechanics. The only information lost in this specialization is the number of loops of M . We show that the coefficients of YM (1 − p, t) are very simply related to the ranks of the Whitney homology groups of the opposite partial orders of the independe...
متن کاملFixing Numbers for Matroids
Motivated by work in graph theory, we define the fixing number for a matroid. We give upper and lower bounds for fixing numbers for a general matroid in terms of the size and maximum orbit size (under the action of the matroid automorphism group). We prove the fixing numbers for the cycle matroid and bicircular matroid associated with 3-connected graphs are identical. Many of these results have...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1993
ISSN: 0095-8956
DOI: 10.1006/jctb.1993.1056