scholarly journals Qlick Graphs with Crossing Number One

2016 ◽  
Vol 17 ◽  
pp. 75-84
Author(s):  
Bommanahal Basavanagoud ◽  
V.R. Kulli
Keyword(s):  
Crossing Number ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Forbidden Subgraphs ◽  
Necessary And Sufficient

In this paper, we deduce a necessary and sufficient condition for graphs whose qlick graphs have crossing number one. We also obtain a necessary and sufficient condition for qlick graphs to have crossing number one in terms of forbidden subgraphs.

A Criterion for (Non-)Planarity of The Block-Transformation Graph Gαβγ when αβγ = 101

2014 ◽  
Vol 10 ◽  
pp. 38-47 ◽  
Author(s):  
B. Basavanagoud ◽  
Jaishri B. Veeragoudar
Keyword(s):  
General Concept ◽  
Crossing Number ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Vertex Set ◽  
Necessary And Sufficient

The general concept of the block-transformation graph Gαβγ was introduced in [1]. The vertices and blocks of a graph are its members. The block-transformation graph G101 of a graph G is the graph, whose vertex set is the union of vertices and blocks of G, in which two vertices are adjacent whenever the corresponding vertices of G are adjacent or the corresponding blocks of G are nonadjacent or the corresponding members of G are incident. In this paper, we present characterizations of graphs whose block-transformation graphs G101 are planar, outerplanar or minimally nonouterplanar. Further we establish a necessary and sufficient condition for the block-transformation graph G101 to have crossing number one.

scholarly journals Semi-Image Neighborhood Block Graphs with Crossing Numbers

2013 ◽  
Vol 5 (2) ◽  
pp. 295-299
Author(s):  
K. M. Niranjan ◽  
P. Nagaraja ◽  
Lokesh V
Keyword(s):  
Graph Theory ◽  
Crossing Number ◽  
Sufficient Condition ◽  
Block Graph ◽  
Necessary And Sufficient Condition ◽  
Engineering Applications ◽  
Crossing Numbers ◽  
Block Graphs ◽  
Necessary And Sufficient

The advent of graph theory has played a prominent role in wide variety of engineering applications. Minimization of crossing numbers in graphs optimizes its use in many applications. In this paper, we establish the necessary and sufficient condition for Semi-Image neighborhood block graph to have crossing number 3. We also prove that the Semi-Image neighborhood block graph NBI(G) of a graph never has crossing numbers k, where    1 ? k ? 6.Keywords: Semi-Image; Neighborhood block; Crossing numbers.© 2013 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.doi: http://dx.doi.org/10.3329/jsr.v5i2.11019        J. Sci. Res. 5 (2), 295-299 (2013)

scholarly journals Граф блоков

2019 ◽  
Author(s):  
A. Kelkar ◽  
K. Jaysurya ◽  
H.M. Nagesh
Keyword(s):  
Crossing Number ◽  
Sufficient Condition ◽  
Block Graph ◽  
Necessary And Sufficient Condition ◽  
Cut Vertex ◽  
Necessary And Sufficient

The block graph of a graph $G$, written $B(G)$, is the graph whose vertices are the blocks of $G$ and in which two vertices are adjacent whenever the corresponding blocks have a cut-vertex in common. We study the properties of $B(G)$ and present the characterization of graphs whose $B(G)$ are planar, outerplanar, maximal outerplanar, minimally non-outerplanar, Eulerian, and Hamiltonian. A necessary and sufficient condition for $B(G)$ to have crossing number one is also presented.

A Proposed Framework Emphasizing Auditor Reliability over Auditor Independence

2003 ◽  
Vol 17 (3) ◽  
pp. 257-266 ◽  
Author(s):  
Mark H. Taylor ◽  
F. Todd DeZoort ◽  
Edward Munn ◽  
Martha Wetterhall Thomas
Keyword(s):  
Public Interest ◽  
Auditor Independence ◽  
Public Confidence ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Accounting Profession ◽  
The Public ◽  
Necessary And Sufficient

This paper introduces an auditor reliability framework that repositions the role of auditor independence in the accounting profession. The framework is motivated in part by widespread confusion about independence and the auditing profession's continuing problems with managing independence and inspiring public confidence. We use philosophical, theoretical, and professional arguments to argue that the public interest will be best served by reprioritizing professional and ethical objectives to establish reliability in fact and appearance as the cornerstone of the profession, rather than relationship-based independence in fact and appearance. This revised framework requires three foundation elements to control subjectivity in auditors' judgments and decisions: independence, integrity, and expertise. Each element is a necessary but not sufficient condition for maximizing objectivity. Objectivity, in turn, is a necessary and sufficient condition for achieving and maintaining reliability in fact and appearance.

The Power of Public Positions

2018 ◽  
Author(s):  
Thomas Sinclair
Keyword(s):  
Detailed Analysis ◽  
Political Authority ◽  
The State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
State Institutions ◽  
State Of Nature ◽  
Necessary And Sufficient

The Kantian account of political authority holds that the state is a necessary and sufficient condition of our freedom. We cannot be free outside the state, Kantians argue, because any attempt to have the “acquired rights” necessary for our freedom implicates us in objectionable relations of dependence on private judgment. Only in the state can this problem be overcome. But it is not clear how mere institutions could make the necessary difference, and contemporary Kantians have not offered compelling explanations. A detailed analysis is presented of the problems Kantians identify with the state of nature and the objections they face in claiming that the state overcomes them. A response is sketched on behalf of Kantians. The key idea is that under state institutions, a person can make claims of acquired right without presupposing that she is by nature exceptional in her capacity to bind others.

scholarly journals Lorentz Boosts and Wigner Rotations: Self-Adjoint Complexified Quaternions

Physics ◽  
2021 ◽  
Vol 3 (2) ◽  
pp. 352-366
Author(s):  
Thomas Berry ◽  
Matt Visser
Keyword(s):  
Point Of View ◽  
Sufficient Condition ◽  
Use Of Self ◽  
Necessary And Sufficient Condition ◽  
Wigner Rotation ◽  
Inertial Frames ◽  
Explicit Formulae ◽  
Specific Implementation ◽  
Necessary And Sufficient ◽  
Lorentz Boosts

In this paper, Lorentz boosts and Wigner rotations are considered from a (complexified) quaternionic point of view. It is demonstrated that, for a suitably defined self-adjoint complex quaternionic 4-velocity, pure Lorentz boosts can be phrased in terms of the quaternion square root of the relative 4-velocity connecting the two inertial frames. Straightforward computations then lead to quite explicit and relatively simple algebraic formulae for the composition of 4-velocities and the Wigner angle. The Wigner rotation is subsequently related to the generic non-associativity of the composition of three 4-velocities, and a necessary and sufficient condition is developed for the associativity to hold. Finally, the authors relate the composition of 4-velocities to a specific implementation of the Baker–Campbell–Hausdorff theorem. As compared to ordinary 4×4 Lorentz transformations, the use of self-adjoint complexified quaternions leads, from a computational view, to storage savings and more rapid computations, and from a pedagogical view to to relatively simple and explicit formulae.

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