 Locating eigenvalues of unbalanced unicyclic signed graphsFrancesco Belardo, Maurizio Brunetti and Vilmar Trevisan Applied Mathematics and Computation, 2021, vol. 400, issue C Abstract: A signed graph is a pair Γ=(G,σ), where G is a graph, and σ:E(G)⟶{+1,−1} is a signature of the edges of G. A signed graph Γ is said to be unbalanced if there exists a cycle in Γ with an odd number of negatively signed edges. In this paper it is presented a linear time algorithm which computes the inertia indices of an unbalanced unicyclic signed graph. Additionally, the algorithm computes the number of eigenvalues in a given real interval by operating directly on the graph, so that the adjacency matrix is not needed explicitly. As an application, the algorithm is employed to check the integrality of some infinite families of unbalanced unicyclic graphs. In particular, the multiplicities of eigenvalues of signed circular caterpillars are studied, getting a geometric characterization of those which are non-singular and sufficient conditions for them to be non-integral. Finally, the algorithm is also used to retrieve the spectrum of bidegreed signed circular caterpillars, none of which turns out to be integral. Keywords: Adjacency matrix; Signature; Inertia indices; Eigenvalue localization; Integral; Circular caterpillars (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:400:y:2021:i:c:s0096300321001302 DOI: 10.1016/j.amc.2021.126082 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.