منابع مشابه
On the Cover Polynomial of a Digraph
There are many polynomials which can be associated with a graph G, the most well known perhaps being the Tutte polynomial T (G; x, y) (cf. [B74] or [T54]). In particular, for specific values of x and y, T (G; x, y) enumerates various features of G. For example, T (G; 1, 1) is just the number of spanning trees of G, T (G; 2, 0) is the number of acyclic orientations of G, T (G; 1, 2) is the numbe...
متن کاملThe drop polynomial of a weighted digraph
Article history: Received 22 February 2016 Available online 23 April 2017 Given a directed graph D = (V, E) with n vertices and a permutation π : V → V on its vertices, we say that π has a drop at a vertex u ∈ V is (u, π(u)) is an edge of D. Letting 〈 D k 〉 denote the number of permutations on V with precisely k drops, we can define the binomial drop polynomial BD(x) = ∑ k 〈 D k 〉( x+k n ) . In...
متن کاملA characterization of the adjacency matrix of the line digraph of a regular digraph
A characterization of the adjacency matrix of the line digraph of a regular digraph is given. Some corollaries are observed.
متن کاملOn the structure of the adjacency matrix of the line digraph of a regular digraph
We show that the adjacency matrix M of the line digraph of a d-regular digraph D on n vertices can be written as M = AB, where the matrix A is the Kronecker product of the all-ones matrix of dimension d with the identity matrix of dimension n and the matrix B is the direct sum of the adjacency matrices of the factors in a dicycle factorization of D.
متن کاملextensions of some polynomial inequalities to the polar derivative
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1971
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1971.38.325