the minimum estrada index of spiro compounds with k quadrangles

Abstract. let g = (v,e) be a finite and simple graph with λ1, λ2,...,λn as its eigenvalues.the estrada index of g is ee(g) =∑ni=1e^{λi} . a spiro compound is a chemical compound that presents a twisted structure of two or more rings, in which 2 or 3 rings are linked together by one common atom. in this paper, we show that the symmetric and stable spiro compounds among all spiro compounds have the minimum estrada index.