Authors: Stevanović, Dragan 
Indulal, Gopalapillai
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: The distance spectrum and energy of the compositions of regular graphs
Journal: Applied Mathematics Letters
Volume: 22
Issue: 7
First page: 1136
Last page: 1140
Issue Date: 1-Jul-2009
Rank: M22
ISSN: 0893-9659
DOI: 10.1016/j.aml.2008.11.007
The distance energy of a graph G is a recently developed energy-type invariant, defined as the absolute deviation of the eigenvalues of the distance matrix of G. It is a useful molecular descriptor in QSPR modelling, as demonstrated by Consonni and Todeschini in [V. Consonni, R. Todeschini, New spectral indices for molecule description, MATCH Commun. Math. Comput. Chem. 60 (2008) 3-14]. We describe here the distance spectrum and energy of the join-based compositions of regular graphs in terms of their adjacency spectrum. These results are used to show that there exist a number of families of sets of noncospectral graphs with equal distance energy, such that for any n ∈ N, each family contains a set with at least n graphs. The simplest such family consists of sets of complete bipartite graphs.
Keywords: Distance energy | Distance spectrum | Join | Regular graphs
Publisher: Elsevier
Project: Serbian Ministry of Science, grant 144015G
Slovenian Agency for Research, program P1-0285

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