A characteristic polynomial for rooted mixed graphs
نویسندگان
چکیده
منابع مشابه
A 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 کاملOn the greedoid polynomial for rooted graphs and rooted digraphs
We examine some properties of the 2-variable greedoid polynomial f(G;t, z) when G is the branching greedoid associated to a rooted graph or a rooted directed graph. For rooted digraphs, we show a factoring property of f (G;t ,z) determines whether or not the rooted digraph has a directed cycle.
متن کاملRelationship between Coefficients of Characteristic Polynomial and Matching Polynomial of Regular Graphs and its Applications
ABSTRACT. Suppose G is a graph, A(G) its adjacency matrix and f(G, x)=x^n+a_(n-1)x^(n-1)+... is the characteristic polynomial of G. The matching polynomial of G is defined as M(G, x) = x^n-m(G,1)x^(n-2) + ... where m(G,k) is the number of k-matchings in G. In this paper, we determine the relationship between 2k-th coefficient of characteristic polynomial, a_(2k), and k-th coefficient of matchin...
متن کاملComputing the Characteristic Polynomial of Threshold Graphs
We present an algorithm for constructing the characteristic polynomial of a threshold graph’s adjacency matrix. The algorithm is based on a diagonalization procedure that is easy to describe. It can be implemented using O(n) space and with running time O(n). Submitted: December 2013 Reviewed: October 2014 Revised: November 2014 Accepted: December 2014 Final: December 2014 Published: December 20...
متن کاملChordal graphs and the characteristic polynomial
A characteristic polynomial was recently de!ned for greedoids, generalizing the notion for matroids. When chordal graphs are viewed as antimatroids by shelling of simplicial vertices, the greedoid characteristic polynomial gives additional information about those graphs. In particular, the characteristic polynomial for a chordal graph is an alternating clique generating function and is expressi...
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: Discrete Mathematics
سال: 2005
ISSN: 0012-365X
DOI: 10.1016/j.disc.2005.09.011