On ordering of minimal energies in bicyclic signed graphs

S. Pirzada; Tahir Shamsher; Mushtaq A. Bhat

doi:10.2478/ausi-2021-0005

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On ordering of minimal energies in bicyclic signed graphs

Acta Universitatis Sapientiae, Informatica

Volume 13 (2021): Issue 1 (June 2021)

By: S. Pirzada, Tahir Shamsher and Mushtaq A. Bhat

Open Access

|Jul 2021

Abstract

Let S = (G, σ) be a signed graph of order n and size m and let x₁, x₂, ..., x_n 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.

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Articles in this issue

DOI: https://doi.org/10.2478/ausi-2021-0005 | Journal eISSN: 2066-7760

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Language: English

Page range: 86 - 121

Submitted on: Mar 22, 2021

Accepted on: Apr 5, 2021

Published online: Jul 8, 2021

Published in print: Jun 1, 2021

Published by: Sapientia Hungarian University of Transylvania

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

Bicyclic signed graph,

balance,

spectrum,

signed energy,

ordering

MSC:

05C22,

05C50,

05C76

Related subjects:

Computer sciences,

Computer sciences, other

© 2021 S. Pirzada, Tahir Shamsher, Mushtaq A. Bhat, published by Sapientia Hungarian University of Transylvania
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 13 (2021): Issue 1 (June 2021)