Lower Bounds for Estrada Index
نویسندگان
چکیده
If G is an (n,m)-graph whose spectrum consists of the numbers λ1, λ2, . . . , λn, then its Estrada index is EE(G) = ∑n i=1 e λi . We establish lower bounds for EE(G) in terms of n and m. Introduction In this paper we are concerned with simple graphs, that have no loops and no multiple or directed edges. Let G be such a graph, and let n and m be the number of its vertices and edges. Then we say that G is an (n,m)-graph. The spectrum of G is the spectrum of its adjacency matrix [1], and consists of the (real) numbers λ1, λ2, . . . , λn. The number n0 of zeros in the spectrum of the graph G is called its nullity. A recently introduced [3, 5] spectrum-based graph invariant is
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