The tau constant and the edge connectivity of a metrized graph
The electronic journal of combinatorics, Tome 19 (2012) no. 4
The tau constant is an important invariant of a metrized graph. It has connections to other graph invariants such as Kirchhoff index, and it has applications to arithmetic properties of algebraic curves. We show how the tau constant of a metrized graph changes under successive edge contractions and deletions. We prove identities which we call "contraction", "deletion", and "contraction-deletion" identities on a metrized graph. By establishing a lower bound for the tau constant in terms of the edge connectivity, we prove that Baker and Rumely's lower bound conjecture on the tau constant holds for metrized graphs with edge connectivity 5 or more. We show that proving this conjecture for 3-regular graphs is enough to prove it for all graphs.
DOI :
10.37236/2934
Classification :
05C40, 05C12, 94C99, 05C76
Mots-clés : metrized graphs, tau constant of metrized graphs, resistance function, contraction identities, deletion identities, contraction-deletion identities, edge connectivity
Mots-clés : metrized graphs, tau constant of metrized graphs, resistance function, contraction identities, deletion identities, contraction-deletion identities, edge connectivity
Affiliations des auteurs :
Zubeyir Cinkir 1
@article{10_37236_2934,
author = {Zubeyir Cinkir},
title = {The tau constant and the edge connectivity of a metrized graph},
journal = {The electronic journal of combinatorics},
year = {2012},
volume = {19},
number = {4},
doi = {10.37236/2934},
zbl = {1266.05077},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2934/}
}
Zubeyir Cinkir. The tau constant and the edge connectivity of a metrized graph. The electronic journal of combinatorics, Tome 19 (2012) no. 4. doi: 10.37236/2934
Cité par Sources :