Groups with complete prime graph connected components

2004 ◽  
Vol 7 (3) ◽  
Author(s):  
Maria Silvia Lucido ◽  
Ali Reza Moghaddamfar
Keyword(s):  
Prime Graph ◽  
Connected Components

scholarly journals On Thompson’s Conjecture for Alternating GroupsAp+3

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Shitian Liu ◽  
Yong Yang
Keyword(s):  
Finite Group ◽  
Prime Graph ◽  
Conjugacy Classes ◽  
Connected Components ◽  
Prime Divisors ◽  
Vertex Set ◽  
Thompson’S Conjecture ◽  
Trivial Center ◽  
A Finite Group

LetGbe a group. Denote byπ(G)the set of prime divisors of|G|. LetGK(G)be the graph with vertex setπ(G)such that two primespandqinπ(G)are joined by an edge ifGhas an element of orderp·q. We sets(G)to denote the number of connected components of the prime graphGK(G). Denote byN(G)the set of nonidentity orders of conjugacy classes of elements inG. Alavi and Daneshkhah proved that the groups,Anwheren=p,p+1,p+2withs(G)≥2, are characterized byN(G). As a development of these topics, we will prove that ifGis a finite group with trivial center andN(G)=N(Ap+3)withp+2composite, thenGis isomorphic toAp+3.

The algorithm of the color signal recognition at landing an unmanned aerial vehicle on an aircraft carrier in autonomous mode

2020 ◽  
pp. 78
Keyword(s):  
Unmanned Aerial Vehicle ◽  
Treatment Method ◽  
Recognition Algorithm ◽  
Connected Components ◽  
Preliminary Treatment ◽  
Signal Recognition ◽  
Aircraft Carrier ◽  
Halftone Image ◽  
Glide Path ◽  
Aerial Vehicle

The movement along the glide path of an unmanned aerial vehicle during landing on an aircraft carrier is investigated. The implementation of this task is realized in the conditions of radio silence of the aircraft carrier. The algorithm for treatment information from an optical landing system installed on an aircraft carrier is developed. The algorithm of the color signal recognition assumes the usage of the image frame preliminary treatment method via a downsample function, that performs the decimation process, the HSV model, the Otsu’s method for calculating the binarization threshold for a halftone image, and the method of separating the connected Two-Pass components. Keywords unmanned aerial vehicle; aircraft carrier; approach; glide path; optical landing system; color signal recognition algorithm; decimation; connected components; halftone image binarization

scholarly journals Upperbounds on the probability of finding marked connected components using quantum walks

2021 ◽  
Vol 20 (1) ◽  
Author(s):  
Adam Glos ◽  
Nikolajs Nahimovs ◽  
Konstantin Balakirev ◽  
Kamil Khadiev
Keyword(s):  
Quantum Walks ◽  
Connected Components

AN EFFICIENT DISTRIBUTED ALGORITHM FOR 3-EDGE-CONNECTIVITY

2006 ◽  
Vol 17 (03) ◽  
pp. 677-701 ◽  
Author(s):  
YUNG H. TSIN
Keyword(s):  
Distributed Algorithm ◽  
Computer Network ◽  
Connected Components ◽  
Message Complexity ◽  
Edge Connectivity ◽  
Worst Case ◽  
Dense Networks

A distributed algorithm for finding the cut-edges and the 3-edge-connected components of an asynchronous computer network is presented. For a network with n nodes and m links, the algorithm has worst-case [Formula: see text] time and O(m + nhT) message complexity, where hT < n. The algorithm is message optimal when [Formula: see text] which includes dense networks (i.e. m ∈ Θ(n2)). The previously best known distributed algorithm has a worst-case O(n3) time and message complexity.

scholarly journals Groups with the Same Prime Graph as the Simple Group D n (5)

2014 ◽  
Vol 66 (5) ◽  
pp. 666-677
Author(s):  
A. Babai ◽  
B. Khosravi
Keyword(s):  
Simple Group ◽  
Prime Graph ◽  
Group D

EXTENDING RESULTS OF MORGAN AND PARKER ABOUT COMMUTING GRAPHS

2021 ◽  
pp. 1-9
Author(s):  
NICOLAS F. BEIKE ◽  
RACHEL CARLETON ◽  
DAVID G. COSTANZO ◽  
COLIN HEATH ◽  
MARK L. LEWIS ◽  
...  
Keyword(s):  
Frobenius Group ◽  
Connected Components ◽  
Commuting Graph

Abstract Morgan and Parker proved that if G is a group with ${\textbf{Z}(G)} = 1$ , then the connected components of the commuting graph of G have diameter at most $10$ . Parker proved that if, in addition, G is solvable, then the commuting graph of G is disconnected if and only if G is a Frobenius group or a $2$ -Frobenius group, and if the commuting graph of G is connected, then its diameter is at most $8$ . We prove that the hypothesis $Z (G) = 1$ in these results can be replaced with $G' \cap {\textbf{Z}(G)} = 1$ . We also prove that if G is solvable and $G/{\textbf{Z}(G)}$ is either a Frobenius group or a $2$ -Frobenius group, then the commuting graph of G is disconnected.

DSP-CC-: I/O Efficient Parallel Computation of Connected Components in Billion-Scale Networks

2015 ◽  
Vol 27 (10) ◽  
pp. 2658-2671 ◽  
Author(s):  
Min-Soo Kim ◽  
Sangyeon Lee ◽  
Wook-Shin Han ◽  
Himchan Park ◽  
Jeong-Hoon Lee
Keyword(s):  
Parallel Computation ◽  
Connected Components
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