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Ars Combinatoria

  • Research article

Bounds of the Sum-connectivity Energy of Graphs

Fuqin Zhan1,2, Youfu Qiao1,2, Junliang Cai3
1School of Mathematics and Statistics, Zhaoging University, Zhaoging 526061, P.R.China
2Department of Mathematics, Hechi University, Yizhou 546800, P.R.China
3College of mathematics, Betjing Normal University, Beijing 100875, P.R.China
  • Published: 31/07/2017

Abstract

The sum-connectivity energy of a graph is defined as the sum of the absolute value of all the eigenvalues of its sum-connectivity matrix. In this paper, we give further lower and upper bounds for the sum-connectivity energy in terms of the number of vertices, number of edges, the harmonic index, and determinant of the sum-connectivity matrix. We also show that among connected graphs with \(n\) vertices, the star graph \(K_{1,n-1}\) has the minimum sum-connectivity energy.

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Citation
Fuqin Zhan, Youfu Qiao, Junliang Cai. Bounds of the Sum-connectivity Energy of Graphs[J], Ars Combinatoria, Volume 134. 295-301. .