Finding a minimum equivalent graph of a digraph

Networks ◽  
1982 ◽  
Vol 12 (2) ◽  
pp. 89-100 ◽  
Author(s):  
Silvano Martello ◽  
Paolo Toth
Keyword(s):  
Equivalent Graph

Lightpath reconfiguration management system for IP-over-CWDM networks with ROADMs, based on equivalent graph method

2009 ◽  
Author(s):  
Raja Zahilah ◽  
Soichiro Nishiuma ◽  
Md. Nooruzzaman ◽  
Nguyen Thi Thanh Thuy ◽  
Osanori Koyama ◽  
...  
Keyword(s):  
Management System ◽  
Graph Method ◽  
Equivalent Graph

An Algorithm for Finding a Minimum Equivalent Graph of a Digraph

1969 ◽  
Vol 16 (3) ◽  
pp. 455-460 ◽  
Author(s):  
Dennis M. Moyles ◽  
Gerald L. Thompson
Keyword(s):  
Equivalent Graph

scholarly journals Mapping graph state orbits under local complementation

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 305
Author(s):  
Jeremy C. Adcock ◽  
Sam Morley-Short ◽  
Axel Dahlberg ◽  
Joshua W. Silverstone
Keyword(s):  
Quantum Computing ◽  
Graph Theory ◽  
Quantum Entanglement ◽  
Graph State ◽  
Graph States ◽  
Potential Applications ◽  
Graph Operation ◽  
Local Complementation ◽  
Equivalent Graph ◽  
Component Graph

Graph states, and the entanglement they posses, are central to modern quantum computing and communications architectures. Local complementation – the graph operation that links all local-Clifford equivalent graph states – allows us to classify all stabiliser states by their entanglement. Here, we study the structure of the orbits generated by local complementation, mapping them up to 9 qubits and revealing a rich hidden structure. We provide programs to compute these orbits, along with our data for each of the 587 orbits up to 9 qubits and a means to visualise them. We find direct links between the connectivity of certain orbits with the entanglement properties of their component graph states. Furthermore, we observe the correlations between graph-theoretical orbit properties, such as diameter and colourability, with Schmidt measure and preparation complexity and suggest potential applications. It is well known that graph theory and quantum entanglement have strong interplay – our exploration deepens this relationship, providing new tools with which to probe the nature of entanglement.

Estimation of sparse equivalent graph filters with limited observations

2017 ◽  
Author(s):  
Shengda Jin ◽  
Zhaowei Zhu ◽  
Xuming Song ◽  
Sadiq Ali ◽  
Hua Qian ◽  
...  
Keyword(s):  
Equivalent Graph

scholarly journals Counting single-qubit Clifford equivalent graph states is #P-complete

2020 ◽  
Vol 61 (2) ◽  
pp. 022202 ◽  
Author(s):  
Axel Dahlberg ◽  
Jonas Helsen ◽  
Stephanie Wehner
Keyword(s):  
Graph States ◽  
Single Qubit ◽  
Equivalent Graph

Trees and Tree-Equivalent Graphs

1965 ◽  
Vol 17 ◽  
pp. 731-733 ◽  
Author(s):  
C. Ramanujacharyulu
Keyword(s):  
Connected Graph ◽  
Connected Components ◽  
Cyclomatic Number ◽  
Equivalent Graph ◽  
Theory Of Graphs

As is well known in the theory of graphs a tree is a connected graph without cycles. Many characterizing properties of trees are known (1), for example the cyclomatic number is equal to zero, which is also equal to p — 1, where p is the number of connected components of the graph. The graphs with cyclomatic number equal to p — 1 are defined here as tree-equivalent graphs. A tree is always a tree-equivalent graph but not conversely. The properties of tree-equivalent graphs are studied here.

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