Signed spectral Turań type theorems

Mahato, Rajesh K. (2023) Signed spectral Turań type theorems. Linear Algebra and Its Applications, 663. pp. 62-79. ISSN 0024-3795

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Abstract

A signed graph Σ=(G,σ) is a graph where the function σ assigns either 1 or −1 to each edge of the simple graph G. The adjacency matrix of Σ, denoted by A(Σ), is defined canonically. In a recent paper, Wang et al. extended the spectral bounds of Hoffman and Cvetković for the chromatic number of signed graphs. They proposed an open problem related to the balanced clique number and the largest eigenvalue of a signed graph. We solve a strengthened version of this open problem. As a byproduct, we give alternate proofs for some of the known classical bounds for the least eigenvalues of unsigned graphs. We extend the Turán's inequality for the signed graphs. Besides, we study the Bollobás and Nikiforov conjecture for the signed graphs and show that the conjecture need not be true for the signed graphs. Nevertheless, the conjecture holds for signed graphs under some assumptions. Finally, we study some of the relationships between the number of signed walks and the largest eigenvalue of a signed graph.

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IITH Creators:

IITH Creators	ORCiD
Mahato, Rajesh K.	http://www.orcid.org/0000-0001-8038-1795

Item Type:

Article

Uncontrolled Keywords:

Balanced clique number; Edge bipartiteness; Eigenvalue; Signed graph; Signed walk; Balanced clique number; Bipartiteness; Clique number; Edge bipartiteness; Eigen-value; Graph G; Largest eigenvalues; Signed graphs; Signed walk; Simple++; Graph theory; Graphic methods; Eigenvalues and eigenfunctions

Subjects:

Mathematics
Mathematics > Algebra

Divisions:

Department of Mathematics

Depositing User:

Mr Nigam Prasad Bisoyi

Date Deposited:

11 Sep 2023 03:58

Last Modified:

11 Sep 2023 03:58

URI:

http://raiithold.iith.ac.in/id/eprint/11662