Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Spectra of Indu–Bala product of graphs and some new pairs of cospectral graphs
View through CrossRef
Recently Indulal and Balakrishnan [Distance spectrum of Indu–Bala product of graphs, AKCE Int. J. Graph Comb. 13 (2016) 230–234] put forward a new graph operation, namely, the Indu–Bala product [Formula: see text] of graphs [Formula: see text] and [Formula: see text], and it is obtained from two disjoint copies of the join [Formula: see text] of [Formula: see text] and [Formula: see text] by joining the corresponding vertices in the two copies of [Formula: see text]. In this paper, we obtain the adjacency spectra, the Laplacian spectra and the signless Laplacian spectra of [Formula: see text] in terms of the corresponding spectra of [Formula: see text] and [Formula: see text]. As applications, these results enable us to construct infinitely many pairs of respective cospectral graphs. Further, the Laplacian spectra enable us to get the formulas of the number of spanning trees and Kirchhoff index of [Formula: see text] in terms of the Laplacian spectra of regular graphs [Formula: see text] and [Formula: see text].
World Scientific Pub Co Pte Lt
Title: Spectra of Indu–Bala product of graphs and some new pairs of cospectral graphs
Description:
Recently Indulal and Balakrishnan [Distance spectrum of Indu–Bala product of graphs, AKCE Int.
J.
Graph Comb.
13 (2016) 230–234] put forward a new graph operation, namely, the Indu–Bala product [Formula: see text] of graphs [Formula: see text] and [Formula: see text], and it is obtained from two disjoint copies of the join [Formula: see text] of [Formula: see text] and [Formula: see text] by joining the corresponding vertices in the two copies of [Formula: see text].
In this paper, we obtain the adjacency spectra, the Laplacian spectra and the signless Laplacian spectra of [Formula: see text] in terms of the corresponding spectra of [Formula: see text] and [Formula: see text].
As applications, these results enable us to construct infinitely many pairs of respective cospectral graphs.
Further, the Laplacian spectra enable us to get the formulas of the number of spanning trees and Kirchhoff index of [Formula: see text] in terms of the Laplacian spectra of regular graphs [Formula: see text] and [Formula: see text].
Related Results
On the reciprocal distance spectrum of edge corona of graphs
On the reciprocal distance spectrum of edge corona of graphs
The reciprocal distance spectrum (Harary spectrum) of a connected graph [Formula: see text] is the multiset of eigenvalues of its reciprocal distance matrix (Harary matrix) [Formul...
Complementary Distance and Reciprocal Complementary Distance Spectrum for Indu-Bala Product of Graphs
Complementary Distance and Reciprocal Complementary Distance Spectrum for Indu-Bala Product of Graphs
For two graphs $G_1$ and $G_2$, graph obtained with two disjoint copies of join structure $G_1 \vee G_2$ by joining the corresponding vertices in $G_2$'s, is the Indu--Bala product...
The spectrum and metric dimension of Indu–Bala product of graphs
The spectrum and metric dimension of Indu–Bala product of graphs
Given a connected graph [Formula: see text], the distance Laplacian matrix [Formula: see text] is defined as [Formula: see text], and the distance signless Laplacian matrix [Formul...
Moderasi Teologi Balā’ Dalam Tafsir Al-Amtsal Nashir Makarim Shiraz: Respon Atas Fatalisme Dan Eskapisme
Moderasi Teologi Balā’ Dalam Tafsir Al-Amtsal Nashir Makarim Shiraz: Respon Atas Fatalisme Dan Eskapisme
Fatalism and escapism are two human responses to the occurrence of balā' from two conflicting theological perspectives, namely the Ash'ariyah who view balā' as an absolute power of...
Construction of Albertson Cospectral and Albertson Equienergetic Graphs Using Graph Operations
Construction of Albertson Cospectral and Albertson Equienergetic Graphs Using Graph Operations
The energy of a graph is an invariant calculated as the sum of the absolute eigenvalues of its adjacency matrix. This concept extends to various types of energies derived from diff...
Reciprocal distance spectrum of Indu-Bala product of
graphs
Reciprocal distance spectrum of Indu-Bala product of
graphs
Let G be a simple connected graph. The reciprocal distance spectrum of G is the multiset of
reciprocal distance eigenvalues of G. The Indu-Bala product G▼H of two graphs G and H i...
An Ingenious Portrayal of Mythical Traits in Bala Graha
An Ingenious Portrayal of Mythical Traits in Bala Graha
Bala grahas, are a group of organisms, very magnificent divine non human forms that have capability to invade human beings and cause diseases attaining different forms and shapes. ...
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...