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The Aα-Spectral Radii of Graphs with Given Connectivity

1,† and 2,*,†
1
School of Mathematics and Statistics and Hubei key Laboratory Mathematics Sciences, Central China Normal University, Wuhan 430079, China
2
Department of Mathematics, Savannah State University, Savannah, GA 31419, USA
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2019, 7(1), 44; https://doi.org/10.3390/math7010044
Received: 22 November 2018 / Revised: 23 December 2018 / Accepted: 24 December 2018 / Published: 4 January 2019
(This article belongs to the Special Issue Graph-Theoretic Problems and Their New Applications)
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PDF [240 KB, uploaded 4 January 2019]

Abstract

The A α -matrix is A α ( G ) = α D ( G ) + ( 1 α ) A ( G ) with α [ 0 , 1 ] , given by Nikiforov in 2017, where A ( G ) is adjacent matrix, and D ( G ) is its diagonal matrix of the degrees of a graph G. The maximal eigenvalue of A α ( G ) is said to be the A α -spectral radius of G. In this work, we determine the graphs with largest A α ( G ) -spectral radius with fixed vertex or edge connectivity. In addition, related extremal graphs are characterized and equations satisfying A α ( G ) -spectral radius are proposed. View Full-Text
Keywords: adjacent matrix; signless Laplacian; spectral radius; connectivity adjacent matrix; signless Laplacian; spectral radius; connectivity
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Wang, C.; Wang, S. The Aα-Spectral Radii of Graphs with Given Connectivity. Mathematics 2019, 7, 44.

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