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Ars Combinatoria

  • Research article

The Minimal Positive Index of Inertia of Signed Unicyclic Graphs

Guihai Yu1,2, Linua Feng3, Qingwen Wang2, Aleksandar Ilié4
1School of Mathematics, Shandong Institute of Business and Technology, Yantai, Shandong, P.R. China, 264005.
2Department of Mathematics, Shanghai University, Shanghai, 200444.
3Department of Mathematics, Central South University, Changsha, Hunan, 410083.
4Faculty of Sciences and Mathematics, University of NiS, Serbia, 18000.
  • Published: 31/01/2014

Abstract

The positive index of inertia of a signed graph \(\Gamma\), denoted by \(,(\Gamma)\), is the number of positive eigenvalues of the adjacency matrix \(A(\Gamma)\) including multiplicities. In this paper we investigate the minimal positive index of inertia of
signed unicyclic graphs of order \(n\) with fixed girth and characterize the extremal graphs with the minimal positive index. Finally, we characterize the signed unicyclic graphs with the positive indices \(1\) and \(2\).

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Citation
Guihai Yu, Linua Feng, Qingwen Wang, Aleksandar Ilié. The Minimal Positive Index of Inertia of Signed Unicyclic Graphs[J], Ars Combinatoria, Volume 117. 245-255. .