Some Upper Bounds for the Net Laplacian Index of a Signed Graph

Abstract

The net Laplacian matrix \(N_{\dot{G}}\) of a signed graph \(\dot{G}\) is defined as \(N_{\dot{G}}=D_{\dot{G}}^{\pm }-A_{\dot{G}}\), where \(D_{\dot{G}}^{\pm }\) and \(A_{\dot{G}}\) denote the diagonal matrix of net-degrees and the adjacency matrix of \(\dot{G}\), respectively. In this study, we give two upper bounds for the largest eigenvalue of \(N_{\dot{G}}\), both expressed in terms related to vertex degrees. We also discuss their quality, provide certain comparisons and consider some particular cases.

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Correspondence to Farzaneh Ramezani.

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Research of the second author is partially supported by Serbian Ministry of Education, Science and Technological Development via Faculty of Mathematics, University of Belgrade.

Communicated by Behruz Tayfeh-Rezaie.

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Ramezani, F., Stanić, Z. Some Upper Bounds for the Net Laplacian Index of a Signed Graph. Bull. Iran. Math. Soc. (2021). https://doi.org/10.1007/s41980-020-00514-2

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Keywords

  • Signed graph
  • Net Laplacian matrix
  • Largest eigenvalue
  • Upper bound

Mathematics Subject Classification

  • 05C22
  • 05C50