The atom-bond connectivity index of graph is a topological index proposed by Estrada et al. as ABC (G)  uvE (G ) (du dv  2) / dudv , where the summation goes over all edges of G, du and dv are the degrees of the terminal vertices u and v of edge uv. In the present paper, some upper bounds for the second type of atom-bond connectivity index are computed.

the atom-bond connectivity index of graph is a topological index proposed by estrada et al.as abc (g)  uve (g ) (du dv  2) / dudv , where the summation goes over all edges ofg, du and dv are the degrees of the terminal vertices u and v of edge uv. in the present paper,some upper bounds for the second type of atom-bond connectivity index are computed.

We introduce a new matrix function for studying graphs and real-world networks based on a double-factorial penalization of walks between nodes in a graph. This new matrix function is based on the matrix error function. We find a very good approximation of this function using a matrix hyperbolic tangent function. We derive a communicability function, a subgraph centrality and a double-factorial ...

X iv :h ep -p h/ 05 11 14 7v 1 1 1 N ov 2 00 5 IPPP/05/67 DCPT/05/134 Studying unquenching effects in QCD with Dyson-Schwinger equations ∗ Christian S. Fischer, Reinhard Alkofer, Wolfgang Cassing, Felipe Llanes-Estrada, Peter Watson, IPPP, University of Durham, Durham DH1 3LE, U.K. Institute of Physics, Graz University, Universitätsplatz 5, A-8010 Graz, Austria Institute for Theoretical Physics...