Computing the maximal signless Laplacian index among graphs of prescribed order and diameter

A bug Bug p,r1r2 is a graph obtained from a complete graph Kp by deleting an edge uv and attaching the paths Pri and Pr2 by one of their end vertices at u and v, respectively. Let Q(G) be the signless Laplacian matrix of a graph G and q1(G) be the spectral radius of Q(G). It is known that the bug<...

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Autores principales:	Abreu,Nair, Lenes,Eber, Rojo,Oscar
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2015
Materias:	Signless Laplacian index diameter bug H-join
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172015000400006
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spelling	oai:scielo:S0716-091720150004000062016-10-25Computing the maximal signless Laplacian index among graphs of prescribed order and diameterAbreu,NairLenes,EberRojo,Oscar Signless Laplacian index diameter bug H-join A bug Bug p,r1r2 is a graph obtained from a complete graph Kp by deleting an edge uv and attaching the paths Pri and Pr2 by one of their end vertices at u and v, respectively. Let Q(G) be the signless Laplacian matrix of a graph G and q1(G) be the spectral radius of Q(G). It is known that the bug<img src="http:/fbpe/img/proy/v34n4//art06_fig1.jpg" width="300" height="59"> maximizes q1(G) among all graphs G of order n and diameter d. For a bug B of order n and diameter d, n - d is an eigenvalue of Q(B) with multiplicity n - d - 1. In this paper, we prove that remainder d +1 eigenvalues of Q(B), among them q1(B), can be computed as the eigenvalues of a symmetric tridiagonal matrix of order d +1. Finally, we show that q1(B0) can be computed as the largest eigenvalue of a symmetric tridiagonal matrix of order<img src="http:/fbpe/img/proy/v34n4//art06_fig2.jpg" width="80" height="56"> whenever d is even.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.34 n.4 20152015-12-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172015000400006en10.4067/S0716-09172015000400006
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Signless Laplacian index diameter bug H-join
spellingShingle	Signless Laplacian index diameter bug H-join Abreu,Nair Lenes,Eber Rojo,Oscar Computing the maximal signless Laplacian index among graphs of prescribed order and diameter
description	A bug Bug p,r1r2 is a graph obtained from a complete graph Kp by deleting an edge uv and attaching the paths Pri and Pr2 by one of their end vertices at u and v, respectively. Let Q(G) be the signless Laplacian matrix of a graph G and q1(G) be the spectral radius of Q(G). It is known that the bug<img src="http:/fbpe/img/proy/v34n4//art06_fig1.jpg" width="300" height="59"> maximizes q1(G) among all graphs G of order n and diameter d. For a bug B of order n and diameter d, n - d is an eigenvalue of Q(B) with multiplicity n - d - 1. In this paper, we prove that remainder d +1 eigenvalues of Q(B), among them q1(B), can be computed as the eigenvalues of a symmetric tridiagonal matrix of order d +1. Finally, we show that q1(B0) can be computed as the largest eigenvalue of a symmetric tridiagonal matrix of order<img src="http:/fbpe/img/proy/v34n4//art06_fig2.jpg" width="80" height="56"> whenever d is even.
author	Abreu,Nair Lenes,Eber Rojo,Oscar
author_facet	Abreu,Nair Lenes,Eber Rojo,Oscar
author_sort	Abreu,Nair
title	Computing the maximal signless Laplacian index among graphs of prescribed order and diameter
title_short	Computing the maximal signless Laplacian index among graphs of prescribed order and diameter
title_full	Computing the maximal signless Laplacian index among graphs of prescribed order and diameter
title_fullStr	Computing the maximal signless Laplacian index among graphs of prescribed order and diameter
title_full_unstemmed	Computing the maximal signless Laplacian index among graphs of prescribed order and diameter
title_sort	computing the maximal signless laplacian index among graphs of prescribed order and diameter
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2015
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172015000400006
work_keys_str_mv	AT abreunair computingthemaximalsignlesslaplacianindexamonggraphsofprescribedorderanddiameter AT leneseber computingthemaximalsignlesslaplacianindexamonggraphsofprescribedorderanddiameter AT rojooscar computingthemaximalsignlesslaplacianindexamonggraphsofprescribedorderanddiameter
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Computing the maximal signless Laplacian index among graphs of prescribed order and diameter

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