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Title: Upper bound for the energy of strongly connected digraphs
Authors: Ayyaswamy S.
Balachandran S.
Gutman I.
Journal: Applicable Analysis and Discrete Mathematics
Issue Date: 1-Apr-2011
Abstract: The energy of a digraph D is dened as E(D), where z1, z2,..., zn are the (possibly complex) eigenvalues of D. We show that if D is a strongly connected digraph on n vertices, a arcs, and c2 closed walks of length two, such that Re(z1) ≥ (a + c2)=(2n) ≥ 1, then E(D) ≤ n(1 + √n)/2. Equality holds if and only if D is a directed strongly regular graph with parameters. This bound extends to digraphs an earlier result [J. H. Koolen, V. Moulton: Maximal energy graphs. Adv. Appl. Math., 26 (2001), 47-52], obtained for simple graphs.
Type: Article
DOI: 10.2298/AADM101121030A
ISSN: 14528630
SCOPUS: 79953303438
Appears in Collections:University Library, Kragujevac
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