<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

Published Online: Jul 08, 2021

Page range: 86 - 121

Received: Mar 22, 2021

Accepted: Apr 05, 2021

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

Keywords
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

Published Online: Jul 08, 2021

Page range: 86 - 121

Received: Mar 22, 2021

Accepted: Apr 05, 2021

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

KeywordsBicyclic 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.

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