Spectra of graphs obtained by a generalization of the join graph operation

Cardoso, Domingos M.; Freitas, Maria Aguieiras A. de; Andrade, Enide; Robbiano, María

doi:10.1016/j.disc.2012.10.016

Cited by 100 publications

(70 citation statements)

References 7 publications

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“…The following generalization of the join operation was introduced by Sabidussi in the 1960s [38] and recently considered in [6]:…”

Section: Join Graph Operationsmentioning

confidence: 99%

“…The spectrum of H[T ] was obtained in [1], and by using an alternative approach that generalizes a lemma by Fiedler [23], also in [6]. …”

Section: Join Graph Operationsmentioning

confidence: 99%

“…Using Lemma 1, in [1,6] the spectrum of the H-join of regular graphs was characterized. As another application, the Laplacian spectrum of the H-join of arbitrary graphs was determined.…”

Section: Join Graph Operationsmentioning

confidence: 99%

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Graphs with maximum Laplacian and signless Laplacian Estrada index

Gutman

Medina

Pizarro

et al. 2016

Discrete Mathematics

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a b s t r a c tThe Laplacian Estrada index (LEE) and the signless Laplacian Estrada index (SLEE) of a graph G are, respectively, the sum of the exponentials of the eigenvalues of the Laplacian and signless Laplacian matrix of G. The vertex frustration index υ b of a graph G is the minimum number of vertices whose deletion from G results in a bipartite graph. Graphs having maximum LEE and SLEE values are determined among graphs with n vertices and 1 ≤ υ b ≤ n − 3.

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“…The following generalization of the join operation was introduced by Sabidussi in the 1960s [38] and recently considered in [6]:…”

Section: Join Graph Operationsmentioning

confidence: 99%

“…The spectrum of H[T ] was obtained in [1], and by using an alternative approach that generalizes a lemma by Fiedler [23], also in [6]. …”

Section: Join Graph Operationsmentioning

confidence: 99%

See 1 more Smart Citation

Graphs with maximum Laplacian and signless Laplacian Estrada index

Gutman

Medina

Pizarro

et al. 2016

Discrete Mathematics

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“…where M j is a symmetric matrix of order n j , for 1 j k. We need introduce the notion of generalized composition, see [4,17]. Let (α 1 j , u 1 j ) be an eigenpair M j , for 1 …”

Section: Lemma 2 (See [14]) If U and W Are Nonadjacent Vertices Of mentioning

confidence: 99%

On matrices associated to directed graphs and applications

Freitas

Bonifácio

Robbiano

et al. 2014

Linear Algebra and its Applications

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MSC: 05C20 05C50 05C76 15A18Keywords: Graphs Incidence matrix (−1, 0, 1)-vertex-edge incidence matrix Line graph Laplacian matrix Signless Laplacian matrix Energy This paper deals with the notions of 0-incidence and 1-incidence between edges on a directed graph associated to the line graph of a graph. The Laplacian energy and the signless Laplacian energy are obtained in a new way. From these results a relation between both energies is derived. Moreover, we obtain lower bounds for both the largest Laplacian eigenvalue and the largest signless Laplacian eigenvalue and prove that the latter is strictly greater than the first one.© 2013 Elsevier Inc. All rights reserved. Notation and preliminariesBy an (n, m)-graph G = (V(G), E(G)), for short G = (V, E), we mean an undirected simple graph on |V| = n vertices and |E| = m edges. If u ∈ V is an end vertex of e ∈ E we say that u incides on e. (M.A.A. de Freitas), andreabonifacio@uniriotec.br (A.S. Bonifácio), mrobbiano@ucn.cl (M. Robbiano), sanmarti@ucn.cl (B. San Martín).

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“…. , H n and the spectrum of a (weighted) adjacency matrix associated to graph G. In [3,8], using different approaches, the L-spectrum of G[H 1 , H 2 , . .…”

Section: Introductionmentioning

confidence: 99%

Lexicographic polynomials of graphs and their spectra

Cardoso

Carvalho

Rama

et al. 2017

APPL ANAL DISCRETE M

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For a (simple) graph H and non-negative integers c0, c1,..., cd (cd ? 0), p(H) = ?dk=0 ck?Hk is the lexicographic polynomial in H of degree d, where the sum of two graphs is their join and ck?Hk is the join of ck copies of Hk. The graph Hk is the kth power of H with respect to the lexicographic product (H0 = K1). The spectrum (if H is connected and regular) and the Laplacian spectrum (in general case) of p(H) are determined in terms of the spectrum of H and ck's. Constructions of infinite families of cospectral or integral graphs are announced. [Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. 174012 Grant no. 174033]

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Spectra of graphs obtained by a generalization of the join graph operation

Abstract: D.M. Cardoso), maguieiras@im.ufrj.br (M.A.A. de Freitas), enide@ua.pt (E.A. Martins), mrobbiano@ucn.cl (M. Robbiano).

Cited by 100 publications

References 7 publications

Graphs with maximum Laplacian and signless Laplacian Estrada index

Graphs with maximum Laplacian and signless Laplacian Estrada index

On matrices associated to directed graphs and applications

Lexicographic polynomials of graphs and their spectra

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