scholarly journals On Mixed Almost Moore Graphs of Diameter Two

10.37236/5647 ◽  
2016 ◽  
Vol 23 (2) ◽  
Author(s):  
Nacho López ◽  
Josep M. Miret
Keyword(s):  
Characteristic Polynomial ◽  
Necessary Conditions ◽  
Directed Graphs ◽  
Cyclotomic Polynomial ◽  
Mixed Case ◽  
Mixed Graphs

Mixed almost Moore graphs appear in the context of the Degree/Diameter problem as a class of extremal mixed graphs, in the sense that their order is one less than the Moore bound for mixed graphs. The problem of their existence has been considered before for directed graphs and undirected ones, but not for the mixed case, which is a kind of generalization. In this paper we give some necessary conditions for the existence of mixed almost Moore graphs of diameter two derived from the factorization in $\mathbb{Q}[x]$ of their characteristic polynomial. In this context, we deal with the irreducibility of $\Phi_i(x^2+x-(r-1))$, where $\Phi_i(x)$ denotes the i-th cyclotomic polynomial.

scholarly journals Determinantal Generalizations of Instrumental Variables

2018 ◽  
Vol 6 (1) ◽  
Author(s):  
Luca Weihs ◽  
Bill Robinson ◽  
Emilie Dufresne ◽  
Jennifer Kenkel ◽  
Kaie Kubjas Reginald McGee II ◽  
...  
Keyword(s):  
Covariance Matrix ◽  
Random Vector ◽  
Instrumental Variables ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Necessary Conditions ◽  
Mixed Graph ◽  
Linear Relationships ◽  
Sufficient And Necessary Conditions ◽  
Mixed Graphs

AbstractLinear structural equation models relate the components of a random vector using linear interdependencies and Gaussian noise. Each such model can be naturally associated with a mixed graph whose vertices correspond to the components of the random vector. The graph contains directed edges that represent the linear relationships between components, and bidirected edges that encode unobserved confounding. We study the problem of generic identifiability, that is, whether a generic choice of linear and confounding effects can be uniquely recovered from the joint covariance matrix of the observed random vector. An existing combinatorial criterion for establishing generic identifiability is the half-trek criterion (HTC), which uses the existence of trek systems in the mixed graph to iteratively discover generically invertible linear equation systems in polynomial time. By focusing on edges one at a time, we establish new sufficient and new necessary conditions for generic identifiability of edge effects extending those of the HTC. In particular, we show how edge coefficients can be recovered as quotients of subdeterminants of the covariance matrix, which constitutes a determinantal generalization of formulas obtained when using instrumental variables for identification. While our results do not completely close the gap between existing sufficient and necessary conditions we find, empirically, that our results allow us to prove the generic identifiability of many more mixed graphs than the prior state-of-the-art.

scholarly journals A characteristic polynomial for rooted mixed graphs

2005 ◽  
Vol 304 (1-3) ◽  
pp. 121-127
Author(s):  
Steven J. Tedford
Keyword(s):  
Characteristic Polynomial ◽  
Mixed Graphs

On the Laplacian characteristic polynomials of mixed graphs

2015 ◽  
Vol 30 ◽  
Author(s):  
Dariush Kiani ◽  
Maryam Mirzakhah
Keyword(s):  
Lower Bound ◽  
Spectral Radius ◽  
Characteristic Polynomial ◽  
Laplacian Matrix ◽  
Characteristic Polynomials ◽  
Laplacian Spectral Radius ◽  
Mixed Graph ◽  
First Derivative ◽  
Signless Laplacian ◽  
Mixed Graphs

Let G be a mixed graph and L(G) be the Laplacian matrix of G. In this paper, the coefficients of the Laplacian characteristic polynomial of G are studied. The first derivative of the characteristic polynomial of L(G) is explicitly expressed by means of Laplacian characteristic polynomials of its edge deleted subgraphs. As a consequence, it is shown that the Laplacian characteristic polynomial of a mixed graph is reconstructible from the collection of the Laplacian characteristic polynomials of its edge deleted subgraphs. Then, it is investigated how graph modifications affect the mixed Laplacian characteristic polynomial. Also, a connection between the Laplacian characteristic polynomial of a non-singular connected mixed graph and the signless Laplacian characteristic polynomial is provided, and it is used to establish a lower bound for the spectral radius of L(G). Finally, using Coates digraphs, the perturbation of the mixed Laplacian spectral radius under some graph transformations is discussed.

Disorientation Affects Mixed-Case More Than UPPERCASE Words

1992 ◽  
Author(s):  
Kevin Jordan ◽  
Laree A. Huntsman
Keyword(s):  
Mixed Case

Czech National Awareness in Moravia in the Revolutionary Years 1848/1849

2014 ◽  
Vol 6 (1) ◽  
Author(s):  
František Čapka
Keyword(s):  
Nineteenth Century ◽  
Necessary Conditions ◽  
Cultural Contact ◽  
Significant Change ◽  
Mutual Relations ◽  
High Degree

AbstractThis study focuses on the process of the gradual shaping of Czech national awareness in Moravia from the beginning of the nineteenth century onwards when the necessary conditions for the development of improved mutual relations between the Czech (Slavic) population in the two Lands of the Czech Crown -Bohemia and Moravia - were slowly being formed. Moravia faced a number of handicaps to the development of a national revival in comparison with Bohemia, the most significant of which was the relatively high degree of Germanisation of the land. A change to the image of Moravia came in the revolutionary years 1848/1849, when Czech national awareness spread to broader sections of society in Moravia. The view of Bohemia held by the Moravians underwent significant change and a period of increasingly intensive political and cultural contact between the two lands arose.

SOCIAL PROTECTION IS A GUARANTEE OF FAMILY UNITY

2020 ◽  
Vol 7 (3) ◽  
pp. 89-96
Author(s):  
Dilbar Karshieva ◽  
Keyword(s):  
Social Protection ◽  
Necessary Conditions ◽  
Family Members ◽  
The State ◽  
The Military ◽  
Family Unity

This article demonstrates the great attention and care paid by the state to the military and their families in our country.Social protection of families of military men consists in creating necessary conditions for family members to develop and demonstrate their abilities in socio-economic, cultural, medical and other spheres.

An Extension of ABC Matrix and ABC Energy for Mixed Graphs

2018 ◽  
Vol 9 (6) ◽  
pp. 513-519
Author(s):  
A. Bharali
Keyword(s):  
Mixed Graphs
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