EMIS ELibM Electronic Journals Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques naturelles / sciences mathematiques
Vol. CXXXIV, No. 32, pp. 33–41 (2007)

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Estrada index of iterated line graphs

Tatjana Aleksic, I. Gutman and M. Petrovic

Faculty of Science, University of Kragujevac, P. O. Box 60, 34000 Kragujevac, Serbia

Abstract: If $\lambda_1,\lambda_2,\ldots,\lambda_n$ are the eigenvalues of a graph $G$ , then the Estrada index of $G$ is $EE(G) = \sum\limits_{i=1}^n e^{\lambda_i}$ . If $L(G) = L^1(G)$ is the line graph of $G$ , then the iterated line graphs of $G$ are defined as $L^k(G) = L(L^{k-1}(G))$ for $k=2,3,\ldots$ . Let $G$ be a regular graph of order $n$ and degree $r$ . We show that $EE(L^k(G)) = a_k(r) EE(G) + n b_k(r)$ , where the multipliers $a_k(r)$ and $b_k(r)$ depend only on the parameters $r$ and $k$ . The main properties of $a_k(r)$ and $b_k(r)$ are established.

Keywords: spectrum (of graph), Estrada index (of graph), regular graph, line graph, complex networks

Classification (MSC2000): 05C50

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Electronic fulltext finalized on: 23 Sep 2007. This page was last modified: 20 Jun 2011.

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