The distance spectrum and energy of the compositions of regular graphs

Stevanović, Dragan; Indulal, Gopalapillai

doi:10.1016/j.aml.2008.11.007

Cited by 64 publications

(23 citation statements)

References 6 publications

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“…In [19] the authors obtain the eigenvalues of the distance matrix of the join of two graphs whose diameter is less than or equal to two, and construct pairs of non D-cospectral, D-equienergetic graphs on n vertices for all n 9. Stevanović and Indulal [20] further generalized this result and described the distance spectrum and energy of the join-based compositions of regular graphs in terms of their adjacency spectrum. Those results are used to show that there exist a number of families of sets of non-cospectral graphs with equal distance energy, such that for any n ∈ N , each family contains a set with at least n graphs.…”

Section: Introductionmentioning

confidence: 94%

Distance spectra and distance energy of integral circulant graphs

Ilić

2010

Linear Algebra and its Applications

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The distance energy of a graph G is a recently developed energy-type invariant, defined as the sum of absolute values of the eigenvalues of the distance matrix of G. There was a vast research for the pairs and families of non-cospectral graphs having equal distance energy, and most of these constructions were based on the join of graphs. A graph is called circulant if it is Cayley graph on the circulant group, i.e. its adjacency matrix is circulant. A graph is called integral if all eigenvalues of its adjacency matrix are integers. Integral circulant graphs play an important role in modeling quantum spin networks supporting the perfect state transfer. In this paper, we characterize the distance spectra of integral circulant graphs and prove that these graphs have integral eigenvalues of distance matrix D. Furthermore, we calculate the distance spectra and distance energy of unitary Cayley graphs. In conclusion, we present two families of pairs (G 1 , G 2 ) of integral circulant graphs with equal distance energy -in the first family G 1 is subgraph of G 2 , while in the second family the diameter of both graphs is three.

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Section: Introductionmentioning

confidence: 94%

Distance spectra and distance energy of integral circulant graphs

Ilić

2010

Linear Algebra and its Applications

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“…The reader can refer, for instance, to the monograph [5] for an exhaustive treatment of spectra of graphs. We also want to mention the papers [24,25,34], where the distance spectrum of some graph compositions has been studied.…”

Section: Introductionmentioning

confidence: 99%

Spectrum, distance spectrum, and Wiener index of wreath products of complete graphs

Donno

2017

Ars Math. Contemp.

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“…Caporossi, Chasser and Furtula in [2] conjectured the closed formula for the distance energy of complete multipartite graphs (see Theorem 2). This conjectured formula was con rmed for the case of bipartite graphs by Stevanovic and Indulal in [6]. Later Stevanovic, Milosevic, Hic and Pokorny in [7] proved the full conjecture.…”

Section: D(g) = [D Ij ] Of G By D Ij = Dist(i J) ≥ If I ≠ J Otherwmentioning

confidence: 78%

A shorter proof of the distance energy of complete multipartite graphs

2017

Special Matrices

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Caporossi, Chasser and Furtula in [Les Cahiers du GERAD (2009) G-2009 conjectured that the distance energy of a complete multipartite graph of order n with r ≥ parts, each of size at least 2, is equal to (n − r). Stevanovic, Milosevic, Hic and Pokorny in [MATCH Commun. Math. Comput. Chem. 70 (2013), no. 1, 157-162.] proved the conjecture, and then Zhang in [Linear Algebra Appl. 450 (2014), 108-120.] gave another proof. We give a shorter proof of this conjecture using the interlacing inequalities of a positve semi-de nite rank-1 perturbation to a real symmetric matrix.

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The distance spectrum and energy of the compositions of regular graphs

Cited by 64 publications

References 6 publications

Distance spectra and distance energy of integral circulant graphs

Distance spectra and distance energy of integral circulant graphs

Spectrum, distance spectrum, and Wiener index of wreath products of complete graphs

A shorter proof of the distance energy of complete multipartite graphs

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