<abstract xmlns="http://www.w3.org/1999/xhtml">

Let S = (G, σ) be a signed graph of order n and size m and let x1, x2, ..., xn be the eigenvalues of S. The energy of S is defined as <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ausi-2021-0005_eq_001.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>ɛ</mi><mrow><mo>(</mo><mi>S</mi><mo>)</mo></mrow><mo>=</mo><munderover><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mrow><mrow><mo>|</mo> <mrow><msub><mrow><mi>x</mi></mrow><mi>j</mi></msub></mrow> <mo>|</mo></mrow></mrow></mrow></math>
<tex-math>\varepsilon \left( S \right) = \sum\limits_{j = 1}^n {\left| {{x_j}} \right|}</tex-math>
</alternatives>
</inline-formula>. A connected signed graph is said to be bicyclic if m=n + 1. In this paper, we determine the bicyclic signed graphs with first 20 minimal energies for all n ≥ 30 and with first 16 minimal energies for all 17 ≤ n ≤ 29.
</abstract>

Let S = (G, σ) be a signed graph of order n and size m and let x1, x2, ..., xn be the eigenvalues of S. The energy of S is defined as 


ɛ(S)=∑j=1n| xj |
\varepsilon \left( S \right) = \sum\limits_{j = 1}^n {\left| {{x_j}} \right|}

. A connected signed graph is said to be bicyclic if m=n + 1. In this paper, we determine the bicyclic signed graphs with first 20 minimal energies for all n ≥ 30 and with first 16 minimal energies for all 17 ≤ n ≤ 29.

On ordering of minimal energies in bicyclic signed graphs

Acta Universitatis Sapientiae, Informatica

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"On ordering of minimal energies in bicyclic signed graphs"}

Let S = (G, σ) be a signed graph of order n and size m and let x1, x2, ..., xn be the eigenvalues of S. The energy of S is defined as 


ɛ(S)=∑j=1n| xj...

On ordering of minimal energies in bicyclic signed graphs

Online veröffentlicht: 08. Juli 2021

Seitenbereich: 86 - 121

Eingereicht: 22. März 2021

Akzeptiert: 05. Apr. 2021

DOI: https://doi.org/10.2478/ausi-2021-0005

Schlüsselwörter
Bicyclic signed graph, balance, spectrum, signed energy, ordering

© 2021 S. Pirzada et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

On ordering of minimal energies in bicyclic signed graphs

Online veröffentlicht: 08. Juli 2021

Seitenbereich: 86 - 121

Eingereicht: 22. März 2021

Akzeptiert: 05. Apr. 2021

DOI: https://doi.org/10.2478/ausi-2021-0005

SchlüsselwörterBicyclic signed graph, balance, spectrum, signed energy, ordering

© 2021 S. Pirzada et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Schlüsselwörter
Bicyclic signed graph, balance, spectrum, signed energy, ordering