scholarly journals Characterizations of line graphs in signed and gain graphs

2022 ◽  
Vol 102 ◽  
pp. 103479
Author(s):  
Matteo Cavaleri ◽  
Daniele D’Angeli ◽  
Alfredo Donno
Keyword(s):  
Line Graphs ◽  
Gain Graphs

scholarly journals Oriented gain graphs, line graphs and eigenvalues

2016 ◽  
Vol 506 ◽  
pp. 316-328 ◽  
Author(s):  
Nathan Reff
Keyword(s):  
Line Graphs ◽  
Gain Graphs

scholarly journals Line graphs of complex unit gain graphs with least eigenvalue -2

2021 ◽  
Vol 37 (37) ◽  
pp. 14-30
Author(s):  
Maurizio Brunetti ◽  
Francesco Belardo
Keyword(s):  
Real Number ◽  
Adjacency Matrix ◽  
Multiplicative Group ◽  
Line Graph ◽  
Line Graphs ◽  
Signed Graphs ◽  
The Real ◽  
Least Eigenvalue ◽  
Gain Graphs ◽  
Gain Graph

Let $\mathbb T$ be the multiplicative group of complex units, and let $\mathcal L (\Phi)$ denote a line graph of a $\mathbb{T}$-gain graph $\Phi$. Similarly to what happens in the context of signed graphs, the real number $\min Spec(A(\mathcal L (\Phi))$, that is, the smallest eigenvalue of the adjacency matrix of $\mathcal L(\Phi)$, is not less than $-2$. The structural conditions on $\Phi$ ensuring that $\min Spec(A(\mathcal L (\Phi))=-2$ are identified. When such conditions are fulfilled, bases of the $-2$-eigenspace are constructed with the aid of the star complement technique.

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 The properties of anti-fuzzy line graphs regular

2021 ◽  
Vol 1872 (1) ◽  
pp. 012010
Author(s):  
Y Trisanti ◽  
T Nusantara
Keyword(s):  
Line Graphs

On maximal energy of line graphs with given parameters

2021 ◽  
Vol 619 ◽  
pp. 12-49
Author(s):  
Yiting Cai ◽  
Bo Zhou ◽  
Mengmeng Gao
Keyword(s):  
Line Graphs ◽  
Maximal Energy

Strongly even cycle decomposable 4-regular line graphs

2021 ◽  
Vol 94 ◽  
pp. 103315
Author(s):  
Wenzhong Liu ◽  
Jiancheng Wang ◽  
Qing Cui ◽  
Yan Yang
Keyword(s):  
Line Graphs ◽  
Regular Line

scholarly journals Topological invariants for the line graphs of some classes of graphs

2019 ◽  
Vol 17 (1) ◽  
pp. 1483-1490
Author(s):  
Xiaoqing Zhou ◽  
Mustafa Habib ◽  
Tariq Javeed Zia ◽  
Asim Naseem ◽  
Anila Hanif ◽  
...  
Keyword(s):  
Communication Theory ◽  
Chemical Reactivity ◽  
Line Graph ◽  
Chemical Properties ◽  
Topological Invariants ◽  
Line Graphs ◽  
Physical And Chemical Properties ◽  
Physical And Chemical ◽  
Ladder Graphs ◽  
And Chemical Properties

AbstractGraph theory plays important roles in the fields of electronic and electrical engineering. For example, it is critical in signal processing, networking, communication theory, and many other important topics. A topological index (TI) is a real number attached to graph networks and correlates the chemical networks with physical and chemical properties, as well as with chemical reactivity. In this paper, our aim is to compute degree-dependent TIs for the line graph of the Wheel and Ladder graphs. To perform these computations, we first computed M-polynomials and then from the M-polynomials we recovered nine degree-dependent TIs for the line graph of the Wheel and Ladder graphs.

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