New upper bounds for Estrada index of bipartite graphs

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.

Estrada Index of Random Bipartite Graphs

The topological structures of many social, biological, and technological systems can be characterized by the connectivity properties of the interaction pathways (edges) between system components (vertices) [1]. Starting with the Königsberg seven-bridge problem in 1736, graphs with bidirectional or symmetric edges have ideally epitomized structures of various complex systems, and have developed ...

Some Lower Bounds for Estrada Index

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 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 ...