Showing papers by "Richard A. Brualdi published in 2012"
TL;DR: In this article, the problem of finding an n × n real symmetric matrix that has a principal submatrix of rank k if and only if r k = 1, for all 0 ⩽ k⩽ n, was studied.
26 citations
TL;DR: In this paper, the authors introduced and investigated the more general class A ( B | S ) of integral matrices with given column sum vector S and with rows that satisfy majorization constraints: each row is majorized by a given vector.
8 citations
TL;DR: In this paper, the authors generalize some basic results for the term rank to the t -term rank, including a formula for the maximum term rank over a nonempty class of ( 0, 1 ) -matrices with the same row sum and column sum vectors.
6 citations
01 Jan 2012
TL;DR: In this article, the authors define the cyclic matching sequencibility of a graph to be the largest integer d such that there exists a cyclic ordering of its edges such that every d consecutive edges in the ordering form a matching.
Abstract: We define the cyclic matching sequencibility of a graph to be the largest integer d such that there exists a cyclic ordering of its edges so that every d consecutive edges in the cyclic ordering form a matching. We show that the cyclic matching sequencibility of K2m and K2m+1 equals m− 1.
4 citations
TL;DR: In this paper, a new permutation statistic was introduced, namely the number of cycles of length q consisting of consecutive integers, and the distribution of this statistic among the permutations of {1, 2,..., n}.
Abstract: We introduce a new permutation statistic, namely, the number of cycles of length q consisting of consecutive integers, and consider the distribution of this statistic among the permutations of {1, 2, . . . , n}. We determine explicit formulas, recurrence relations, and ordinary and exponential generating functions. A generalization to more than one fixed length is also considered.
4 citations
TL;DR: In this paper, the minimum and maximum energy of the classes of weighted trees and forests with positive integral weights and fixed total weight sum m, respectively, were derived for order n, where n is the number of trees in the graph.
Abstract: Let 𝒯(n, m) and ℱ(n, m) denote the classes of weighted trees and forests, respectively, of order n with the positive integral weights and the fixed total weight sum m, respectively. In this article, we determine the minimum energies for both the classes 𝒯(n, m) and ℱ(n, m). We also determine the maximum energy for the class ℱ(n, m). In all cases, we characterize the weighted graphs whose energies reach these extremal values. We also solve the similar maximum energy and minimum energy problems for the classes of (0, 1) weighted trees and forests.
2 citations
1 citations