Some Lower Bounds for Estrada Index

some lower bounds for estrada index

Lower Bounds for Estrada Index

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 ...

New Lower Bounds for Estrada Index

Let G be an n-vertex graph. If λ1, λ2, . . . , λn are the adjacency eigenvalues of G, then the Estrada index and the energy of G are defined as EE(G) = ∑n i=1 e λi and E(G) = ∑n i=1 |λi|, respectively. Some new lower bounds for EE(G) are obtained in terms of E(G). We also prove that if G has m edges and t triangles, then EE(G) ≥ √ n2 + 2mn+ 2nt. The new lower bounds improve previous lower bound...

Lower bounds for the Estrada index

Ela Lower Bounds for the Estrada Index of Graphs

The Estrada index was used to study the folding degree of proteins and other long-chain molecules [4, 5, 6, 9]. It also has numerous applications in the vast field of complex networks [7, 8, 13, 14, 17]. A number of properties especially lower and upper bounds [3, 10, 11, 12, 15, 16, 18, 19, 20] for the Estrada index are known. In this paper, we establish further lower bounds improving some res...

Bounds of distance Estrada index of graphs

Let λ1, λ2, · · · , λn be the eigenvalues of the distance matrix of a connected graph G. The distance Estrada index of G is defined as DEE(G) = ∑ n i=1 ei . In this note, we present new lower and upper bounds for DEE(G). In addition, a Nordhaus-Gaddum type inequality for DEE(G) is given. MSC 2010: 05C12, 15A42.