Pedro Bicudo, Stephen Cotanch, Felipe Llanes-Estrada, Pieter Maris, Emilio Ribeiro, and Adam Szczepaniak Departamento de Fı́sica, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal Department of Physics, North Carolina State University, Raleigh, North Carolina 27695-8202 Departamento de Fı́sica Teórica I, Univ. Complutense de Madrid, 28040 Madrid, Spain Physics Department and...

Let G be a simple graph of order n, let λ1(G), λ2(G), . . . , λn(G) be the eigenvalues of the adjacency matrix of G. The Esrada index of G is defined as EE(G) = ∑n i=1 e i. In this paper we determine the unique graph with maximum Estrada index among bicyclic graphs with fixed order.

The atom bond connectivity index of a graph is a new topological index was defined by E. Estrada as ABC(G)  uvE (dG(u) dG(v) 2) / dG(u)dG(v) , where G d ( u ) denotes degree of vertex u. In this paper we present some bounds of this new topological index.

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 ...