On Complex Eigenvalues of M and P Matrices.
On composition of signed graphs
A graph whose edges are labeled either as positive or negative is called a signed graph. In this article, we extend the notion of composition of (unsigned) graphs (also called lexicographic product) to signed graphs. We employ Kronecker product of matrices to express the adjacency matrix of this product of two signed graphs and hence find its eigenvalues when the second graph under composition is net-regular. A signed graph is said to be net-regular if every vertex has constant net-degree, namely,...
On computing the distinguishing numbers of trees and forests.
On concentration of self-bounding functions.
On conditional independence and log-convexity
If conditional independence constraints define a family of positive distributions that is log-convex then this family turns out to be a Markov model over an undirected graph. This is proved for the distributions on products of finite sets and for the regular Gaussian ones. As a consequence, the assertion known as Brook factorization theorem, Hammersley–Clifford theorem or Gibbs–Markov equivalence is obtained.
On congruence properties of the partition function.
On connected graphs containing exactly two points of the same degree
On connected graphs with maximal index.
On connected resolving decompositions in graphs
For an ordered -decomposition of a connected graph and an edge of , the -code of is the -tuple , where is the distance from to . A decomposition is resolving if every two distinct edges of have distinct -codes. The minimum for which has a resolving -decomposition is its decomposition dimension . A resolving decomposition of is connected if each is connected for . The minimum for which has a connected resolving -decomposition is its connected decomposition...
On connectedness of graphs on direct product of Weyl groups
In this paper, we have studied the connectedness of the graphs on the direct product of the Weyl groups. We have shown that the number of the connected components of the graph on the direct product of the Weyl groups is equal to the product of the numbers of the connected components of the graphs on the factors of the direct product. In particular, we show that the graph on the direct product of the Weyl groups is connected iff the graph on each factor of the direct product is connected.
On connectedness of graphs on Weyl groups of type ()
On connection between the structure of a finite group and the properties of its prime graph.
On connections between hypergraphs and algebras
The aim of the present paper is to translate some algebraic concepts to hypergraphs. Thus we obtain a new language, very useful in the investigation of subalgebra lattices of partial, and also total, algebras. In this paper we solve three such problems on subalgebra lattices, other will be solved in [[Pio4]]. First, we show that for two arbitrary partial algebras, if their directed hypergraphs are isomorphic, then their weak, relative and strong subalgebra lattices are isomorphic. Secondly, we prove...
On constant-weight TSP-tours
Is it possible to label the edges of Kₙ with distinct integer weights so that every Hamilton cycle has the same total weight? We give a local condition characterizing the labellings that witness this question's perhaps surprising affirmative answer. More generally, we address the question that arises when "Hamilton cycle" is replaced by "k-factor" for nonnegative integers k. Such edge-labellings are in correspondence with certain vertex-labellings, and the link allows us to determine (up to a constant...
On convexity of polynomial paths and generalized majorizations.
On coset coverings of solutions of homogeneous cubic equations over finite fields.
On cotree-critical and DFS cotree-critical graphs.
On counting of periodic words. (Zur Abzählung periodischer Worte.)
On counting permutations by pairs of congruence classes of major index.
On covering of bounded sets by sets with the twice less diameter