Polynomial Tutte Invariants of Rooted Integral Gain Graphs
نویسندگان
چکیده
We present dichromatic and tree-expansion polynomials of integral gain graphs that underlie the problem of counting lattice points in the complement of an integral affinographic hyperplane arrangement. This is a step towards finding the universal Tutte invariant of rooted integral gain graphs. Mathematics Subject Classifications (2000): Primary 05C22; Secondary 05C15.
منابع مشابه
Colorations, Orthotopes, and a Huge Polynomial Tutte Invariant of Weighted Gain Graphs
A gain graph is a graph whose edges are labelled invertibly from a group. A weighted gain graph is a gain graph with vertex weights from a semigroup, where the gain group is lattice ordered and acts on the weight semigroup. For weighted gain graphs we establish basic properties and we present general dichromatic and tree-expansion polynomials that are Tutte invariants (they satisfy Tutte’s dele...
متن کاملLattice Points in Orthotopes and a Huge Polynomial Tutte Invariant of Weighted Gain Graphs Version of January 4, 2016
A gain graph is a graph whose edges are orientably labelled from a group. A weighted gain graph is a gain graph with vertex weights from an abelian semigroup, where the gain group is lattice ordered and acts on the weight semigroup. For weighted gain graphs we establish basic properties and we present general dichromatic and forest-expansion polynomials that are Tutte invariants (they satisfy T...
متن کاملLattice points in orthotopes and a huge polynomial Tutte invariant of weighted gain graphs
A gain graph is a graph whose edges are orientably labelled from a group. A weighted gain graph is a gain graph with vertex weights from an abelian semigroup, where the gain group is lattice ordered and acts on the weight semigroup. For weighted gain graphs we establish basic properties and we present general dichromatic and forest-expansion polynomials that are Tutte invariants (they satisfy T...
متن کاملHomomorphisms and Polynomial Invariants of Graphs
This paper initiates a study of the connection between graph homomorphisms and the Tutte polynomial. This connection enables us to extend the study to other important polynomial invariants associated with graphs, and closely related to the Tutte polynomial. We then obtain applications of these relationships in several areas, including Abelian Groups and Statistical Physics. A new type of unique...
متن کامل