On the relation between the adjacency rank of a complex unit gain graph and the matching number of its underlying graph

2020 ◽  
pp. 1-20
Author(s):  
Shuchao Li ◽  
Ting Yang
Keyword(s):  
Matching Number ◽  
Underlying Graph ◽  
Gain Graph

scholarly journals The rank of a complex unit gain graph in terms of the rank of its underlying graph

2019 ◽  
Vol 38 (2) ◽  
pp. 570-588 ◽  
Author(s):  
Yong Lu ◽  
Ligong Wang ◽  
Qiannan Zhou
Keyword(s):  
Underlying Graph ◽  
Gain Graph

scholarly journals The rank of a complex unit gain graph in terms of the matching number

2020 ◽  
Vol 589 ◽  
pp. 158-185 ◽  
Author(s):  
Shengjie He ◽  
Rong-Xia Hao ◽  
Fengming Dong
Keyword(s):  
Matching Number ◽  
Gain Graph

scholarly journals Graphical splittings of Artin kernels

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Enrique Miguel Barquinero ◽  
Lorenzo Ruffoni ◽  
Kaidi Ye
Keyword(s):  
Free Group ◽  
Artin Group ◽  
Artin Groups ◽  
Graphs Of Groups ◽  
Underlying Graph ◽  
Block Graphs ◽  
Right Angled Artin Groups

Abstract We study Artin kernels, i.e. kernels of discrete characters of right-angled Artin groups, and we show that they decompose as graphs of groups in a way that can be explicitly computed from the underlying graph. When the underlying graph is chordal, we show that every such subgroup either surjects to an infinitely generated free group or is a generalized Baumslag–Solitar group of variable rank. In particular, for block graphs (e.g. trees), we obtain an explicit rank formula and discuss some features of the space of fibrations of the associated right-angled Artin group.

scholarly journals ESTIMATING PURITY AND ENTROPY IN STABILIZER STATE EXPERIMENTS

2010 ◽  
Vol 08 (01n02) ◽  
pp. 325-335 ◽  
Author(s):  
HARALD WUNDERLICH ◽  
MARTIN B. PLENIO
Keyword(s):  
Quantum Information ◽  
Measurement Data ◽  
Simulated Data ◽  
The State ◽  
Graph State ◽  
Graph States ◽  
Underlying Graph ◽  
Moderate Number ◽  
Full State ◽  
State Tomography

Many experiments in quantum information aim at creating graph states. Quantifying the purity of an experimentally achieved graph state could in principle be accomplished using full-state tomography. This method requires a number of measurement settings growing exponentially with the number of constituents involved. Thus, full-state tomography becomes experimentally infeasible even for a moderate number of qubits. In this paper, we present a method to estimate the purity of experimentally achieved graph states with simple measurements. The observables we consider are the stabilizers of the underlying graph. Then, we formulate the problem as: "What is the state with the least purity that is compatible with the measurement data?" We solve this problem analytically and compare the obtained bounds with results from full-state tomography for simulated data.

scholarly journals The size of 3-uniform hypergraphs with given matching number and codegree

2019 ◽  
Vol 342 (3) ◽  
pp. 760-767
Author(s):  
Xinmin Hou ◽  
Lei Yu ◽  
Jun Gao ◽  
Boyuan Liu
Keyword(s):  
Matching Number ◽  
Uniform Hypergraphs

scholarly journals Graphs with restricted valency and matching number

2009 ◽  
Vol 309 (12) ◽  
pp. 4176-4180 ◽  
Author(s):  
Niranjan Balachandran ◽  
Niraj Khare
Keyword(s):  
Matching Number
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