Glossary of Signed and Gain Graphs

10.37236/31 ◽  
2002 ◽  
Vol 1000 ◽  
Author(s):  
Thomas Zaslavsky
Keyword(s):  
Gain Graphs

A glossary to accompany DS8.

scholarly journals Line and Subdivision Graphs Determined by T4-Gain Graphs

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 926 ◽  
Author(s):  
Abdullah Alazemi ◽  
Milica Anđelić ◽  
Francesco Belardo ◽  
Maurizio Brunetti ◽  
Carlos M. da Fonseca
Keyword(s):  
Spectral Properties ◽  
Incidence Matrix ◽  
Multiplicative Group ◽  
Line Graph ◽  
Characteristic Polynomials ◽  
Signed Graphs ◽  
Subdivision Graph ◽  
Gain Graphs ◽  
The Relationship ◽  
Gain Graph

Let T 4 = { ± 1 , ± i } be the subgroup of fourth roots of unity inside T , the multiplicative group of complex units. For a T 4 -gain graph Φ = ( Γ , T 4 , φ ) , we introduce gain functions on its line graph L ( Γ ) and on its subdivision graph S ( Γ ) . The corresponding gain graphs L ( Φ ) and S ( Φ ) are defined up to switching equivalence and generalize the analogous constructions for signed graphs. We discuss some spectral properties of these graphs and in particular we establish the relationship between the Laplacian characteristic polynomial of a gain graph Φ , and the adjacency characteristic polynomials of L ( Φ ) and S ( Φ ) . A suitably defined incidence matrix for T 4 -gain graphs plays an important role in this context.

Subgroup Switching of Skew Gain Graphs

2012 ◽  
Vol 116 (1-4) ◽  
pp. 111-122
Author(s):  
Jurriaan Hage
Keyword(s):  
Gain Graphs

Spectra of quaternion unit gain graphs

2021 ◽  
Author(s):  
Francesco Belardo ◽  
Maurizio Brunetti ◽  
Nolan J. Coble ◽  
Nathan Reff ◽  
Howard Skogman
Keyword(s):  
Gain Graphs

scholarly journals Balancedness and the least Laplacian eigenvalue of some complex unit gain graphs

2020 ◽  
Vol 40 (2) ◽  
pp. 417 ◽  
Author(s):  
Francesco Belardo ◽  
Maurizzo Brunetti ◽  
Nathan Reff
Keyword(s):  
Laplacian Eigenvalue ◽  
Gain Graphs
Sign in / Sign up

Export Citation Format

Share Document