Tetracyclic graphs with maximal Estrada index

Abstract

In this paper, we use the same techniques of [20]. Let G = (V,E) be a simple connected graph of order n = n(G) and size m = m(G). If m = n − 1 + c, then G is called a c-cyclic graph. A graph with c = 4 is referred as a tetracyclic graph. The characteristic polynomial φ(G;x) of G is |xI−A(G)|, where A(G) is the (0, 1)adjacency matrix of G, and I is the unit matrix. We call the eigenvalues λ1(G) ≥ λ2(G) ≥ · · · ≥ λn(G) (for short λ1 ≥ λ2 ≥ · · · ≥ λn) of A(G) the spectrum of G. The Estrada index, put forward by Estrada [6], is defined as EE(G) = ∑n i=1 e λi . In this paper, we consider the Estrada index of tetracyclic graphs, and characterize all tetracyclic graphs of order n with maximal Estrada index. The concept of Estrada index in graphs has found multiple applications in a large variety of problems. For some examples, it has been employed to quantify the degree of folding of long-chain molecules, especially proteins [7, 8], to measure the centrality of complex (reaction, metabolic, communication, social, etc.) networks,

DOI: 10.1142/S1793830917500410

Cite this paper

@article{Rad2017TetracyclicGW, title={Tetracyclic graphs with maximal Estrada index}, author={Nader Jafari Rad and Akbar Jahanbani and Doost Ali Mojdeh}, journal={Discrete Math., Alg. and Appl.}, year={2017}, volume={9}, pages={1-18} }