Journal Article10.1016/j.laa.2022.06.006
On the A-spectral radius of graphs with given size and diameter
Zhiming Feng,Wei Wei +1 more
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TL;DR: In this article , the authors determined the graph having the maximum A α -spectral radius for α ∈ [ 1 2 , 1 ) among all connected graphs of size m and diameter d .
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About: This article is published in Linear Algebra and its Applications. The article was published on 01 Jun 2022. The article focuses on the topics: Spectral radius & RADIUS.
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Citations
Maximizing the signless Laplacian spectral radius of minimally 3-connected graphs with given size
Shu-Guang Guo,Rong Zhang +1 more
TL;DR: Maximizing the signless Laplacian spectral radius of minimally 3-connected graphs with given size. Upper bound and characterization of extremal graphs.
3
On the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e87" altimg="si18.svg"><mml:mi>α</mml:mi></mml:math>-index of minimally 2-connected graphs with given order or size
Jiayu Lou,Ligong Wang,Ming Yuan +2 more
TL;DR: In this article , the authors characterized the extremal graphs with the maximum α-index for α∈[12,1] among all minimally 2-connected graphs with given order or size, respectively.
3
Maxima of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e173" altimg="si15.svg"><mml:msub><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mi>α</mml:mi></mml:mrow></mml:msub></mml:math>-index of graphs with given size and domination number
Rong Zhang,Shuchun Guo +1 more
TL;DR: This paper determines the extremal graphs with maximal Aα-index among all graphs with given size m, domination number γ, and no isolated vertices for α∈[12,1], using the Aα-matrix defined by Nikiforov in 2017.
1
The spread of generalized reciprocal distance matrix
Hechao Liu,Yufei Huang +1 more
- 07 Jul 2022
TL;DR: In this paper , the generalized reciprocal distance matrix RD α (G) was defined as RD α(G) = αRT (G ) + (1 − α ) RD (G ), 0 ≤ α ≤ 1 .
References
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Graph Theory
J. A. Bondy,U.S.R Murty +1 more
- 14 Aug 2008
TL;DR: This book provides a systematic treatment of the theory of graphs without sacrificing its intuitive and aesthetic appeal, and is suitable as a textbook for advanced undergraduate and beginning graduate students in mathematics and computer science.
3.6K
Merging the A-and Q-spectral theories
TL;DR: In this article, a convex linear combination of a graph with adjacency matrix A(G) and a signless Laplacian D(G), defined as Aα (G) := αD(G + (1 - α)A(G)), 0 ≤ α ≤ 1.
On the spectral radius of (0,1)-matrices
TL;DR: In this article, the maximum spectral radius for (0, 1)-matrices with k2 and k2+1 1's, respectively, and for symmetric (1, 1) matrices with zero trace and e=k21's (graphs with e edges) was determined.
182
A Bound on the Spectral Radius of Graphs with e Edges
TL;DR: The spectral radius p(A) of the adjacency matrix A of a graph G with e edges satisfies p (A)
164
On the maximal index of graphs with a prescribed number of edges
TL;DR: Among the graphs with a prescribed number of edges, those with maximal index are determined as discussed by the authors, which confirms a conjecture of Brualdi and Hoffman, and thus confirms the existence of the maximal index conjecture.
102