On the Generalized Distance Energy of Graphs
TLDR
In this article, the generalized distance matrix of a simple connected graph G is defined as a convex combination of the convex combinations of T r (G ) + (1 − α ) D (G) for 0 ≤ α ≤ 1.About:
This article is published in Linear Algebra and its Applications.The article was published on 2019-12-19 and is currently open access. It has received 21 citations till now. The article focuses on the topics: Complete bipartite graph & Bipartite graph.read more
Citations
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On (distance) Laplacian energy and (distance) signless Laplacian energy of graphs
TL;DR: In this article, the Nordhaus-Gaddum type bounds on distance Laplacian energy of graphs and trees of order n of a simple graph G were presented and the extremal graphs for which these bounds were best possible.
Journal ArticleDOI
The Generalized Distance Spectrum of the Join of Graphs
TL;DR: The spectral properties of the generalized distance matrix of graphs, the convex combination of the symmetric distance matrix D ( G) and diagonal matrix of the vertex transmissions T r ( G ) are studied.
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Merging the Spectral Theories of Distance Estrada and Distance Signless Laplacian Estrada Indices of Graphs
TL;DR: In this paper, the generalized distance Estrada index of a graph G is defined as a generalized distance matrix D α (G ) = ∑ i = 1 n e ∂ i − 2 α W ( G ) n, where W denotes the Wiener index of G.
Distance Laplacian eigenvalues and chromatic number in graphs
Mustapha Aouchiche,Pierre Hansen +1 more
TL;DR: In this paper, the authors studied the spectral radius of the distance Laplacian of a connected graph with fixed order and chromatic number and proved lower bounds on the spectral spectral radius in terms of $n$ and $chi.
Journal ArticleDOI
Sharp Bounds on (Generalized) Distance Energy of Graphs
TL;DR: In this paper, the generalized distance matrix D α (G) = α T r (G ) + ( 1 − α ) D (G ), where α ∈ [ 0, 1 ].
References
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Book
Matrix Analysis
Roger A. Horn,Charles R. Johnson +1 more
TL;DR: In this article, the authors present results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrate their importance in a variety of applications, such as linear algebra and matrix theory.
Book
Spectra of graphs : theory and application
TL;DR: The Spectrum and the Group of Automorphisms as discussed by the authors have been used extensively in Graph Spectra Techniques in Graph Theory and Combinatory Applications in Chemistry an Physics. But they have not yet been applied to Graph Spectral Biblgraphy.
Book
A Survey of Matrix Theory and Matrix Inequalities
Marvin Marcus,Henryk Minc +1 more
TL;DR: This book presents an enormous amount of information in a concise and accessible format and begins with the assumption that the reader has never seen a matrix.
Journal ArticleDOI
The energy of a graph
TL;DR: In this article, it was shown that for any positive integer n⩾3, there exist two equienergetic graphs of order 4n that are not cospectral.
Book ChapterDOI
The Energy of a Graph: Old and New Results
TL;DR: In this article, the energy of a graph G is defined as the sum of the absolute values of the eigenvalues of G. The connection between E and the total electron energy of organic molecules is briefly outlined.