Rolling Upward Planarity Testing of Strongly Connected Graphs

2013 ◽  
pp. 38-49 ◽  
Author(s):  
Christopher Auer ◽  
Christian Bachmaier ◽  
Franz J. Brandenburg ◽  
Kathrin Hanauer
Keyword(s):  
Connected Graphs ◽  
Strongly Connected ◽  
Upward Planarity

On kernels in strongly connected graphs

Networks ◽  
1977 ◽  
Vol 7 (3) ◽  
pp. 263-266 ◽  
Author(s):  
M. Anciaux-Mundeleer ◽  
P. Hansen
Keyword(s):  
Connected Graphs ◽  
Strongly Connected

The Exponents of Strongly Connected Graphs

1969 ◽  
Vol 21 ◽  
pp. 769-782 ◽  
Author(s):  
Edward A. Bender ◽  
Thomas W. Tucker
Keyword(s):  
Directed Graph ◽  
Connected Graphs ◽  
Strongly Connected ◽  
Elementary Circuit ◽  
Image Position

A directed graphG is a set of vertices V and a subset of V × V called the edges of G. A path in G of length k,is such that (vi, vi+1) is an edge of G for 1 ≦ i ≦ k. A directed graph G is strongly connected if there is a path from every vertex of G to every other vertex. A circuit is a path whose two end vertices are equal. An elementary circuit has no other equal vertices. See (1) for a fuller discussion.Let G be a finite, strongly connected, directed graph (fscdg). The kth power Gk of G is the directed graph with the same vertices as G and edges of the form (i, j) where G has a path of length k from i to j.

Irreducible economies and strongly connected graphs

2005 ◽  
Vol 41 (8) ◽  
pp. 937-956 ◽  
Author(s):  
Ruth Baldry ◽  
Sayantan Ghosal
Keyword(s):  
Connected Graphs ◽  
Strongly Connected

scholarly journals The number of edges in critical strongly connected graphs

2001 ◽  
Vol 234 (1-3) ◽  
pp. 119-123 ◽  
Author(s):  
Ron Aharoni ◽  
Eli Berger
Keyword(s):  
Connected Graphs ◽  
Strongly Connected

scholarly journals Invariance of KMS states on graph C*-algebras under classical and quantum symmetry

2021 ◽  
pp. 1-17
Author(s):  
Soumalya Joardar ◽  
Arnab Mandal
Keyword(s):  
Automorphism Group ◽  
Automorphism Groups ◽  
Inverse Temperature ◽  
Circulant Graphs ◽  
Connected Graphs ◽  
Kms States ◽  
C Algebras ◽  
Kms State ◽  
Quantum Symmetry ◽  
Strongly Connected

Abstract We study the invariance of KMS states on graph $C^{\ast }$ -algebras coming from strongly connected and circulant graphs under the classical and quantum symmetry of the graphs. We show that the unique KMS state for strongly connected graphs is invariant under the quantum automorphism group of the graph. For circulant graphs, it is shown that the action of classical and quantum automorphism groups preserves only one of the KMS states occurring at the critical inverse temperature. We also give an example of a graph $C^{\ast }$ -algebra having more than one KMS state such that all of them are invariant under the action of classical automorphism group of the graph, but there is a unique KMS state which is invariant under the action of quantum automorphism group of the graph.

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