A Tutte polynomial which distinguishes rooted unicyclic graphs
نویسندگان
چکیده
منابع مشابه
A Greedoid Polynomial Which Distinguishes Rooted Arborescences
We define a two-variable polynomial fa(t, z) for a greedoid G which generalizes the standard one-variable greedoid polynomial A<j(f). Several greedoid invariants (including the number of feasible sets, bases, and spanning sets) are easily shown to be evaluations of fG(t, z). We prove (Theorem 2.8) that when G is a rooted directed arborescence, fo(t, z) completely determines the arborescence. We...
متن کاملPolynomial Tutte Invariants of Rooted Integral Gain Graphs
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.
متن کاملChromatic and Tutte Polynomials for Graphs, Rooted Graphs and Trees
The chromatic polynomial of a graph is a one-variable polynomial that counts the number of ways the vertices of a graph can be properly colored. It was invented in 1912 by G.D. Birkhoff in his unsuccessful attempt to solve the four-color problem. In the 1940’s, Tutte generalized Birkhoff’s polynomial by adding another variable and analyzing its combinatorial properties. The Tutte polynomial its...
متن کاملA Tutte polynomial for signed graphs
This paper introduces a generalization of the Tutte polynomial [14] that is defined for signed graphs. A signed graph is a graph whose edges are each labelled with a sign (+l or 1). The generalized polynomial will be denoted Q[G] = Q[G](A, B, d). Here G is the signed graph, and the letters A, B, d denote three independent polynomial variables. The polynomial Q[G] can be specialized to the Tutte...
متن کاملA characteristic polynomial for rooted graphs and rooted digraphs
We consider the one-variable characteristic polynomial p(G; ) in two settings. When G is a rooted digraph, we show that this polynomial essentially counts the number of sinks in G. When G is a rooted graph, we give combinatorial interpretations of several coe/cients and the degree of p(G; ). In particular, |p(G; 0)| is the number of acyclic orientations of G, while the degree of p(G; ) gives th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2009
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2008.03.007