Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Harary spectra and Harary energy of line graphs of regular graphs
View through CrossRef
The Harary matrix of a graph G is defined as RD(G) = [rij] in which rij = 1 ∕ dij if i ≠ j and rij = 0 if i = j, where dij is the distance between the vertices vi and vj in G. The Harary energy of G is defined as the sum of the absolute values of the eigenvalues of Harary matrix. Two graphs are said to be Harary equienergetic if they have same Harary energy. In this paper we show that the Harary matrix of complement of the line graph of certain regular graphs has exactly one positive eigenvalue. Further we obtain the Harary energy of line graphs and of complement of line graphs of certain regular graphs and thus constructs pairs of Harary equienergetic graphs of same order and having different Harary eigenvalues.
Title: Harary spectra and Harary energy of line graphs of regular graphs
Description:
The Harary matrix of a graph G is defined as RD(G) = [rij] in which rij = 1 ∕ dij if i ≠ j and rij = 0 if i = j, where dij is the distance between the vertices vi and vj in G.
The Harary energy of G is defined as the sum of the absolute values of the eigenvalues of Harary matrix.
Two graphs are said to be Harary equienergetic if they have same Harary energy.
In this paper we show that the Harary matrix of complement of the line graph of certain regular graphs has exactly one positive eigenvalue.
Further we obtain the Harary energy of line graphs and of complement of line graphs of certain regular graphs and thus constructs pairs of Harary equienergetic graphs of same order and having different Harary eigenvalues.
Related Results
Tightness of Harary Graphs
Tightness of Harary Graphs
In the design of real-world networks, researchers evaluate various structural parameters to assess vulnerability, including connectivity, toughness, and tenacity. Recently, the tig...
K-Regular Matroids
K-Regular Matroids
<p>The class of matroids representable over all fields is the class of regular matroids. The class of matroids representable over all fields except perhaps GF(2) is the class...
Hurricane Eloise Directional Wave Energy Spectra
Hurricane Eloise Directional Wave Energy Spectra
ABSTRACT
Directiona1 wave energy spectra, calculated from data recorded during Hurricane Eloise (Gulf of Mexico, 1975), are presented. The spectra, based on an en...
Simplified access of asteroid spectral data and metadata using classy
Simplified access of asteroid spectral data and metadata using classy
Remote-sensing spectroscopy is the most efficient observational technique to characterise the surface composition of asteroids within a reasonable timeframe. While photometry allow...
Spectral Properties of the Harary Signless Laplacian and Harary Incidence Energy
Spectral Properties of the Harary Signless Laplacian and Harary Incidence Energy
Let X be a partitioned matrix and let B its equitable quotient matrix. Consider a simple, undirected, connected graph G of order n. In this paper, we employ a technique based on qu...
Computing the Energy of Certain Graphs based on Vertex Status
Computing the Energy of Certain Graphs based on Vertex Status
Background:
The concept of Hückel molecular orbital theory is used to compute the graph energy numerically and graphically on the base of the status of a vertex.
Objective:
Our a...
[RETRACTED] Keanu Reeves CBD Gummies v1
[RETRACTED] Keanu Reeves CBD Gummies v1
[RETRACTED]Keanu Reeves CBD Gummies ==❱❱ Huge Discounts:[HURRY UP ] Absolute Keanu Reeves CBD Gummies (Available)Order Online Only!! ❰❰= https://www.facebook.com/Keanu-Reeves-CBD-G...
On the node reliability of Harary graphs: an analysis through real-world topologies
On the node reliability of Harary graphs: an analysis through real-world topologies
The literature on network reliability shows that Harary networks are designed so that the link reliability is maximum in many cases. The following question: ``what are the best top...