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Extremal values on the eccentric distance sum of trees
Eccentric distance sum Domination number Leaves Bipartition
2012/7/11
Let $G=(V_G, E_G)$ be a simple connected graph. The eccentric distance sum of $G$ is defined as $\xi^{d}(G) = \sum_{v\in V_G}\varepsilon_{G}(v)D_{G}(v)$, where $\varepsilon_G(v)$ is the eccentricity o...
We present a new approach for counting trees, and we apply it to count multitype Cayley trees and to prove the multivariate Lagrange inversion formula. The gist of our approach is to exploit the symme...
A multivariate hook formula for labelled trees
hook formula tree enumeration representation theory of symmetric groups finite difference operators multivariate Lagrange inversion
2012/5/24
Several hook summation formulae for binary trees have appeared recently in the literature. In this paper we present an analogous formula for unordered increasing trees of size r, which involves r para...
Absolutely symmetric trees and complexity of natural number
Absolutely symmetric trees complexity of natural number Combinatorics
2012/5/24
We consider the rooted trees which not have isomorphic representation and introduce a conception of complexity a natural number also. The connection between quantity such trees with $n$ edges and a co...
Abstract: Extending Furstenberg's ergodic theoretic proof for Szemer\'edi's theorem on arithmetic progressions, Furstenberg and Weiss (2003) proved the following qualitative result. For every d and k,...
Intervals of balanced binary trees in the Tamari lattice
balanced binary tree Tamari lattice poset grammar generating series fixed-point functional equation
2011/9/14
Abstract: We show that the set of balanced binary trees is closed by interval in the Tamari lattice. We establish that the intervals [T, T'] where T and T' are balanced binary trees are isomorphic as ...
On augmented eccentric connectivity index of graphs and trees
eccentric connectivity index Combinatorics graphs and trees
2011/9/2
Abstract: In this paper we establish all extremal graphs with respect to augmented eccentric connectivity index among all (simple connected) graphs, among trees and among trees with perfect matching. ...
Spanning trees and expansions for the Potts model partition function in an external field
Tutte polynomial Potts model spanning trees V -polynomial external field Hamiltonian edge activities
2011/9/5
Abstract: We use a deletion-contraction relation for the variable field Potts model partition function to give an expansion of the variable field Potts model partition function in terms of the zero fi...
Chip-firing games, potential theory on graphs, and spanning trees
Chip-firing games graphs spanning trees Combinatorics
2011/8/26
Abstract: We study the interplay between chip-firing games and potential theory on graphs, characterizing reduced divisors ($G$-parking functions) on graphs as the solution to an energy (or potential)...