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

Estrada index of iterated line graphsTatjana Aleksic, I. Gutman and M. PetrovicFaculty of Science, University of Kragujevac, P. O. Box 60, 34000 Kragujevac, SerbiaAbstract: 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 $L^k(G) = L(L^{k1}(G))$ 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 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 23 Sep 2007. This page was last modified: 20 Jun 2011.
© 2007 Mathematical Institute of the Serbian Academy of Science and Arts
