منابع مشابه
Distance Matrix Polynomials of Trees
Let G be a finite connected graph. If x and y are vertices of G, one may define a distance function d, on G by letting d&x, y) be the minimal length of any path between x and y in G (with d&, x) = 0). Thus, for example, d&x, y) = 1 if and only if {x, y} is an edge of G. Furthermore, we define the distance matrix D(G) for G to be the square matrix with rows and columns indexed by the vertex set ...
متن کاملFactoring distance matrix polynomials
In this paper we prove that a vertex-centered automorphism of a tree gives a proper factor of the characteristic polynomial of its distance or adjacency matrix. We also show that the characteristic polynomial of the distance matrix of any graph always has a factor of degree equal to the number of vertex orbits of the graph. These results are applied to full k-ary trees and some other problems. ...
متن کاملOn the distance from a matrix polynomial to matrix polynomials with two prescribed eigenvalues
Consider an n × <span style="fon...
متن کاملImmanantal Polynomials of Laplacian Matrix of Trees
The immanant d () associated with the irreducible character of the symmetric group S n , indexed by the partition of n, acting on an nn matrix A = a ij ] is deened by d (A) = X 2Sn () n Y i=1 a ii(i) : For a tree T on n vertices, let L(T) denote its Laplacian matrix. Let x be an indeterminate variable and I be the n n identity matrix. The immanantal polynomial of T corresponding to d is deened ...
متن کاملOn the spectra of reduced distance matrix of the generalized Bethe trees
Let G be a simple connected graph and {v_1,v_2,..., v_k} be the set of pendent (vertices of degree one) vertices of G. The reduced distance matrix of G is a square matrix whose (i,j)-entry is the topological distance between v_i and v_j of G. In this paper, we compute the spectrum of the reduced distance matrix of the generalized Bethe trees.
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: Advances in Mathematics
سال: 1978
ISSN: 0001-8708
DOI: 10.1016/0001-8708(78)90005-1