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
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 2 [ m at h . C O ] 8 J ul 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 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 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 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