Search results for "Complement graph"
showing 10 items of 10 documents
About Graph Complements
2020
Summary This article formalizes different variants of the complement graph in the Mizar system [3], based on the formalization of graphs in [6].
Relations between structure and estimators in networks of dynamical systems
2011
The article main focus is on the identification of a graphical model from time series data associated with different interconnected entities. The time series are modeled as realizations of stochastic processes (representing nodes of a graph) linked together via transfer functions (representing the edges of the graph). Both the cases of non-causal and causal links are considered. By using only the measurements of the node outputs and without assuming any prior knowledge of the network topology, a method is provided to estimate the graph connectivity. In particular, it is proven that the method determines links to be present only between a node and its “kins”, where kins of a node consist of …
On the Soluble Graph of a Finite Simple Group
2013
The maximal independent sets of the soluble graph of a finite simple group G are studied and their independence number is determined. In particular, it is shown that this graph in many cases has an independent set with three vertices.
Graph Connectivity, Monadic NP and built-in relations of moderate degree
1995
It has been conjectured [FSV93] that an existential secondoder formula, in which the second-order quantification is restricted to unary relations (i.e. a Monadic NP formula), cannot express Graph Connectivity even in the presence of arbitrary built-in relations.
Highly irregular graphs with extreme numbers of edges
1997
Abstract A simple connected graph is highly irregular if each of its vertices is adjacent only to vertices with distinct degrees. In this paper we find: (1) the greatest number of edges of a highly irregular graph with n vertices, where n is an odd integer (for n even this number is given in [1]), (2) the smallest number of edges of a highly irregular graph of given order.
P-matrix completions under weak symmetry assumptions
2000
An n-by-n matrix is called a Π-matrix if it is one of (weakly) sign-symmetric, positive, nonnegative P-matrix, (weakly) sign-symmetric, positive, nonnegative P0,1-matrix, or Fischer, or Koteljanskii matrix. In this paper, we are interested in Π-matrix completion problems, that is, when a partial Π-matrix has a Π-matrix completion. Here, we prove that a combinatorially symmetric partial positive P-matrix has a positive P-matrix completion if the graph of its specified entries is an n-cycle. In general, a combinatorially symmetric partial Π-matrix has a Π-matrix completion if the graph of its specified entries is a 1-chordal graph. This condition is also necessary for (weakly) sign-symmetric …
Incomplete vertices in the prime graph on conjugacy class sizes of finite groups
2013
Abstract Given a finite group G, consider the prime graph built on the set of conjugacy class sizes of G. Denoting by π 0 the set of vertices of this graph that are not adjacent to at least one other vertex, we show that the Hall π 0 -subgroups of G (which do exist) are metabelian.
Groups whose prime graph on conjugacy class sizes has few complete vertices
2012
Abstract Let G be a finite group, and let Γ ( G ) denote the prime graph built on the set of conjugacy class sizes of G. In this paper, we consider the situation when Γ ( G ) has “few complete vertices”, and our aim is to investigate the influence of this property on the group structure of G. More precisely, assuming that there exists at most one vertex of Γ ( G ) that is adjacent to all the other vertices, we show that G is solvable with Fitting height at most 3 (the bound being the best possible). Moreover, if Γ ( G ) has no complete vertices, then G is a semidirect product of two abelian groups having coprime orders. Finally, we completely characterize the case when Γ ( G ) is a regular …
Temporal aggregation in chain graph models
2005
The dependence structure of an observed process induced by temporal aggregation of a time evolving hidden spatial phenomenon is addressed. Data are described by means of chain graph models and an algorithm to compute the chain graph resulting from the temporal aggregation of a directed acyclic graph is provided. This chain graph is the best graph which covers the independencies of the resulting process within the chain graph class. A sufficient condition that produces a memory loss of the observed process with respect to its hidden origin is analyzed. Some examples are used for illustrating algorithms and results.
Distance graphs and the T-coloring problem
1999
Abstract The T-coloring problem is, given a graph G = (V, E), a set T of nonnegative integers containing 0, and a ‘span’ bound s ⩾ 0, to compute an integer coloring f of the vertices of G such that |f(ν) − f(w)| ∉ T ∀νw ∈ E and max f − min f ⩽ s. This problem arises in the planning of channel assignments for broadcast networks. When restricted to complete graphs, the T-coloring problem boils down to a number problem which can be solved efficiently for many types of sets T. The paper presents results indicating that this is not the case if the set T is arbitrary. To these ends, the class of distance graphs is introduced, which consists of all graphs G : G ≅ G(A) for some (finite) set of posi…