The distance spectrum and energy of the compositions of regular graphs

✍ Scribed by Dragan Stevanović; Gopalapillai Indulal

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 365 KB
• Volume: 22
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/j.aml.2008.11.007

✦ Synopsis

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.