ar X iv : 0 80 5 . 09 92 v 2 [ m at h . C O ] 8 J ul 2 00 8 FIBONACCI IDENTITIES AND GRAPH COLORINGS
نویسنده
چکیده
We generalize both the Fibonacci and Lucas numbers to the context of graph colorings, and prove some identities involving these numbers. As a corollary we obtain new proofs of some known identities involving Fibonacci numbers such as Fr+s+t = Fr+1Fs+1Ft+1 + FrFsFt − Fr−1Fs−1Ft−1.
منابع مشابه
ar X iv : 0 80 5 . 09 92 v 1 [ m at h . C O ] 7 M ay 2 00 8 FIBONACCI IDENTITIES AND GRAPH COLORINGS
We generalize both the Fibonacci and Lucas numbers to the context of graph colorings, and prove some identities involving these numbers. As a corollary we obtain new proofs of some known identities involving Fibonacci numbers such as Fr+s+t = Fr+1Fs+1Ft+1 + FrFsFt − Fr−1Fs−1Ft−1.
متن کاملar X iv : h ep - t h / 05 03 09 9 v 2 1 8 A pr 2 00 5 Cancellation of energy - divergences in Coulomb gauge QCD
In the Coulomb gauge of nonabelian gauge theories there are in general, in individual graphs, ‘energy-divergences’ on integrating over the loop energy variable for fixed loop momentum. These divergences are avoided in the Hamiltonian, phase-space formulation. But, even in this formulation, energy-divergences re-appear at 2-loop order. We show in an example how these cancel between graphs as a c...
متن کاملar X iv : h ep - t h / 05 03 09 9 v 1 1 1 M ar 2 00 5 Cancellation of energy - divergences in Coulomb gauge QCD
In the Coulomb gauge of nonablian gauge theories there are in general, in individual graphs, ‘energy-divergences’ on integrating over the loop energy variable for fixed loop momentum. These divergences are avoided in the Hamiltonian, phase-space formulation. But, even in this formulation, energy-divergences re-appear at 2-loop order. We show in an example how these cancel between graphs as a co...
متن کاملar X iv : 0 70 7 . 23 06 v 1 [ m at h . C O ] 1 6 Ju l 2 00 7 Parity , eulerian subgraphs and the Tutte polynomial
Identities obtained by elementary finite Fourier analysis are used to derive a variety of evaluations of the Tutte polynomial of a graph G on the hyperbolae H 2 and H 4. These evaluations are expressed in terms of eulerian subgraphs of G and the size of subgraphs modulo 2, 3, 4 or 6. In particular, a graph is found to have a nowhere-zero 4-flow if and only if there is a correlation between the ...
متن کاملFibonacci Identities and Graph Colorings
We generalize both the Fibonacci and Lucas numbers to the context of graph colorings, and prove some identities involving these numbers. As a corollary we obtain new proofs of some known identities involving Fibonacci numbers such as Fr+s+t = Fr+1Fs+1Ft+1 + FrFsFt − Fr−1Fs−1Ft−1.
متن کامل