Computing the determinant of a signed graph-Reference-Cited by-同舟云学术

Computing the determinant of a signed graph

Published:2024-01-01 Issue:1 Volume:22 Page:
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Alshamary Bader¹,Stanić Zoran²

Affiliation:

1. Department of Mathematics, Kuwait University , Al Shadadiyah , Kuwait

2. Faculty of Mathematics, University of Belgrade , Studentski trg 16 , 11 000 Belgrade , Serbia

Abstract

Abstract A signed graph is a simple graph in which every edge has a positive or negative sign. In this article, we employ several algebraic techniques to compute the determinant of a signed graph in terms of the spectrum of a vertex-deleted subgraph. Particular cases, including vertex-deleted subgraphs without repeated eigenvalues or singular vertex-deleted subgraphs are considered. As applications, an algorithm for the determinant of a signed graph with pendant edges is established, the determinant of a bicyclic graph and the determinant of a chain graph are computed. In the end, the uniqueness of the polynomial reconstruction for chain graphs is proved.

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/math-2023-0188/pdf

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